Federal Customs Service
State educational institution
Higher professional education
"Russian Customs Academy"
Vladivostok branch
Presentation on theme: "Order. Chaos. Entropy Growth"
Completed by students
121 groups: Ilyin D.,
Chernozemov A.
Checked:
Pugach P. A.
Vladivostok 2010
1. Introduction…………………………………………………………….. 3
2. Orderliness……………………………………………………… 4
3. Chaos ............................................... ................................................. ..... five
4. Increasing entropy………………………………………………… 7
5. Conclusion………………………………………………………….. 9
6. References……………………………………………………10
Introduction
All natural processes are accompanied by an increase in the entropy of the Universe; such a statement is often called the entropy principle. Entropy also characterizes the conditions under which energy is stored: if energy is stored at a high temperature, its entropy is relatively low, and its quality, on the contrary, is high. On the other hand, if the same amount of energy is stored at a low temperature, then the entropy associated with this energy is high and its quality is low.
The increase in entropy is hallmark natural processes and corresponds to the storage of energy with more and more low temperatures. Similarly, we can say that the natural direction of the processes of change is characterized by a decrease in the quality of energy.
Such an interpretation of the relationship between energy and entropy, in which entropy characterizes the conditions for the storage and storage of energy, is of great importance. practical value. The first law of thermodynamics states that the energy of an isolated system (and possibly the entire universe) remains constant. Therefore, by burning fossil fuels - coal, oil, uranium - we do not reduce the total energy reserves. In this sense, an energy crisis is generally impossible, since the energy in the world will always remain unchanged. However, by burning a handful of coal and a drop of oil, we increase the entropy of the world, since all these processes occur spontaneously. Any action leads to a decrease in the quality of the energy of the Universe. Since the process of using resources is rapidly accelerating in an industrialized society, the entropy of the Universe is steadily increasing. It is necessary to strive to direct the development of civilization along the path of reducing the level of entropy production and maintaining the quality of energy.
orderliness
Orderliness is a characteristic of a structure that indicates the degree of mutual consistency of its elements. In relation to the socio-cognitive system, the characteristic of orderliness corresponds to a high degree of structured knowledge in the context of a concrete historical system of rationality.
The concept of the development of inanimate and living nature is considered as an irreversible directed change in the structure of objects of nature, since the structure reflects the level of organization of matter.
Structure is the internal organization of the system, which contributes to the connection of the elements that make up the system, which determines its existence as a whole and its qualitative features. The structure determines the ordering of the elements of an object. Elements are any phenomena, processes, as well as any properties and relationships that are in some kind of mutual connection and relationship with each other.
The structure is the ordering (compositions) of elements that is preserved (invariant) with respect to certain changes (transformations).
Order is a relatively stable way of linking elements, giving their interaction within the framework of an internally dissected object a holistic character.
The most important property is its relative stability, understood as preservation in change. However, the ordering contains a certain dynamism, separate temporal moments, is a process of deployment in time and space of new properties of elements.
Orderliness is a general, qualitatively defined and relatively stable order of internal relations between the subsystems of a particular system. The concept of "level of organization" in contrast to the concept of "structure" includes, in addition, the idea of changing structures and its sequence in the course of historical development systems since its inception. While the change in structure may be random and not always directed, the change in the level of organization occurs in a necessary way. Systems that have reached an appropriate level of organization and have a certain structure acquire the ability to use information in order to maintain unchanged (or increase) their level of organization through control and contribute to the constancy (or decrease) of their entropy.
Chaos
Etymology of the concept "chaos".
Chaos, a concept that finally took shape in ancient Greek philosophy, is a tragic image of the cosmic primary unity, the beginning and end of everything, the eternal death of all living things and at the same time the principle and source of all development, it is disordered, omnipotent and faceless.
Chaos (Greek cháos, from cháino - I open up, vomit), in ancient Greek mythology, the boundless initial mass, from which everything that exists was subsequently formed. In a figurative sense - a mess, confusion.
Physicists, chemists, biologists, mathematicians, engineers, etc. are interested in chaos. These researchers specialize in systems that exhibit turbulence, are difficult to describe and are of a random nature, that is, they deal with disorder. However, there were some skeptics here. Some mathematicians say that the theoretical methods for studying chaos are loose, based on unreliable models, and threaten traditional ways of testing solutions. Nevertheless, chaos theory has won followers and has its advocates in every major university or research center. This theory offers an approach to the study of systems that cannot be described by traditional methods. For many scientists theory chaos is another way of solving very difficult problems that requires fresh ideas.
Since Newton, scientists have sought to explain behavior complex system with the help of linear (establishing a simple direct dependence) equations that establish a direct proportionality between the value given at the input of the system and the value obtained at the same time at the output of the system. If you know all the variables, they believe, and have a powerful enough computer to take into account all the uncertainties, then you can model (i.e., describe in mathematical terms) any system, no matter how complex it may be. An example would be a long-range weather forecast. Meteorologists were among those who thought that new supercomputers would make long-range weather predictions definitively reliable, but this has not happened. Working on computer models weather, MIT meteorologist Eduard Lorenz has shown that models of chaotic systems depend strongly on initial conditions and minute but unpredictable variables—in other words, weather is inherently chaotic.
In any chaotic system - from a fast-moving mountain river to the average annual locust population in the American Midwest - a slight imbalance can lead to a huge change. "A very small perturbation that occurred at some time can cause the system to develop quite differently than without such a perturbation," says Lorenz. Scientists call this phenomenon the butterfly effect. The name was coined by Lorenz when, in a lecture he gave in 1970, he posed an intriguing question to the audience: could the slight flutter of a butterfly's wings far in the Amazonian jungle cause a devastating tornado in Texas.
The Law of Truth in Chaos:
“Any chaotic (Brownian) movement leads to the formation of meaningful pairs. Couples tend to bond. Or, with the course of the process, meaningfulness and order appear in it. Chaos is far away (myriads and dimyads of light years), but we know its law. So we are from there, or were in it.
These words make sense major problem– Problems of Choice.
Entropy increase
Entropy (Greek en - in, inside, trope - turn, transformation) - one of the quantities characterizing the thermal state of a body or system of bodies; a measure of the internal disorder of the system; for all processes occurring in a closed system, the entropy either increases (irreversible processes) or remains constant (reversible processes).
The central concept of thermodynamics is the entropy S. Entropy is a function of state, the differential of which is equal to the reduced heat dS = dQ/T, where Q is the amount of heat, T is the temperature. Entropy has long been considered the shadow of the "queen-energy" W, its mysterious counterpart. Their behavior in a closed system is different. Energy in a closed system is neither created nor destroyed. It is saved and cannot serve as an indicator of changes in the system (W = const). Entropy is constantly created in any process of transition to equilibrium. The behavior of entropy is determined by the second law of thermodynamics or the law of entropy increase.
The growth of entropy is not unlimited. Its value in equilibrium is maximum. The second law of thermodynamics is the law and principle of selection that limits the physically realizable states that can be observed or "cooked". The law prohibits the creation of a "perpetual motion machine of the 2nd kind."
The famous second law (law) of thermodynamics in the formulation of the German physicist R. Clausius sounds like this: "Heat does not spontaneously transfer from a cold body to a hotter one." The law of conservation and transformation of energy (the first law of thermodynamics), in principle, does not prohibit such a transition, as long as the amount of energy is preserved in the same volume.
But in reality this never happens. This one-sidedness, one-directionality of the redistribution of energy in closed systems is emphasized by the second law of thermodynamics. To reflect this process, a new concept of "entropy" was introduced into thermodynamics. Under entropy, they began to lower the degree of disorder of the system. A more precise formulation of the second law of thermodynamics took the following form: in spontaneous processes in systems with constant energy, entropy always increases. The physical meaning of the increase in entropy boils down to the fact that an isolated (with constant energy) system consisting of a certain set of particles tends to go into a state with the least orderliness of particle motion. This is the simplest state of the system, or thermodynamic equilibrium, in which the motion of particles is chaotic. Maximum entropy means complete thermodynamic equilibrium, which is equivalent to chaos.
However, based on Prigogine's theory of change, entropy is not just a non-stop sliding of the system to a state devoid of any organization. Under certain conditions, entropy
becomes the progenitor of order.
*The macroscopic state of one or another thermodynamic system, consisting of a finite set of elements (atoms, molecules), is traditionally characterized using the Boltzmann entropy (E), which statistically expresses the second law of thermodynamics and has the form:
where: - Boltzmann's constant, and W is the thermodynamic probability, which is the number of possible microstates of the system, through which this macrostate can be realized.
Conclusion
The law of increasing entropy is applicable only to sufficiently large gathering particles, and for individual molecules it is simply impossible to formulate.
Issues related to entropy in complex systems and the law of entropy increase make it possible to objectively perceive the processes occurring in nature and determine the possibilities of intervening in these processes.
The law of increasing entropy is part of the second law of thermodynamics, which is usually called the experimentally obtained statement about the impossibility of building a perpetual motion machine of the second kind.
Bibliography
1. F.Yu. Siegel. The inexhaustibility of infinity. Moscow, "Science", 1984
2. P. Atkins. Order and disorder in nature. Translation from English by Yu.G. Rudogo. Moscow, "Mir", 1987
3. D. Leiser. Creating a picture of the universe. Translation from English by S.A. Lamzin. Moscow, "Mir", 1988
4. J. Narlikar. Furious Universe. Translation from English by S.V. Budnik. Moscow, "Mir", 1985
This group of patterns also characterizes the interaction of the system with its environment - with the environment (significant or essential for the system), supersystem, subordinate systems.
Communication.
This regularity forms the basis for the definition of a system where the system is not isolated from other systems, it is connected by many communications with the environment, which, in turn, is a complex and heterogeneous formation containing a supersystem (a metasystem is a higher order system that sets the requirements and limitations of the system under study). ), subsystems (underlying, subordinate systems), and systems of the same level as the one under consideration.
Such a complex unity with the environment is called regularity of communication, which, in turn, easily helps to move to hierarchy as a pattern of building the whole world and any system separated from it.
Hierarchy.
The laws of hierarchy or hierarchical ordering were among the first laws of systems theory that L. von singled out and studied. Bertalanffy.
It is necessary to take into account not only the external structural side of the hierarchy, but also the functional relationships between levels. For example, in biological organizations, a higher hierarchical level has a guiding effect on the lower level subordinate to it, and this effect is manifested in the fact that the subordinate members of the hierarchy acquire new properties that they did not have in an isolated state (confirmation of the position on the influence of the whole on the elements given above), and as a result of the appearance of these new properties, a new, different “image of the whole” is formed (the influence of the properties of elements on the whole). The new whole that has arisen in this way acquires the ability to perform new functions, which is the purpose of the formation of hierarchies.
Let us single out the main features of hierarchical ordering in terms of the usefulness of their use as systems analysis models:
1. Due to the regularity of communication, which manifests itself not only between the selected system and its environment, but also between the levels of the hierarchy of the system under study, each level of hierarchical ordering has complex relationships with the higher and lower levels. According to the metaphorical formulation, each level of the hierarchy has the property of a “two-faced Janus”: the “face” directed towards the lower level has the character of an autonomous whole (system), and the “face” directed towards the node (top) of the higher level exhibits the properties of a dependent part (element of the higher system).
This concretization of the pattern of hierarchy explains the ambiguity of use in complex organizational systems ah the concepts of "system" and "subsystem", "goal" and "means" (an element of each level of the hierarchical structure of goals acts as a goal in relation to the underlying ones and as a "sub-goal", and starting from a certain level, and as a "means" in relation to to a higher goal), which is often observed in real conditions and leads to incorrect terminological disputes.
2. The most important feature of hierarchical ordering as a regularity is that the regularity of integrity/emergence (i.e., qualitative changes in the properties of components of a higher level compared to the combined components of the underlying one) manifests itself in it at each level of the hierarchy. At the same time, the combination of elements in each node of the hierarchical structure leads not only to the appearance of new properties for the node and the loss of the freedom of manifestation of some of its properties by the combined components, but also to the fact that each subordinate member of the hierarchy acquires new properties that were absent in its isolated state.
1. Basic concepts of systems theory (definition of a system, environment, object, element; system of representations)
System - this is a complete, integral set of elements (components), interconnected and interacting with each other so that the function of the system can be realized.
The study of an object as a system involves the usea number of representation systems (categories), among which the main ones are:
Structural representation is associated with the selection of the elements of the system and the links between them.
Functional representation of systems - the allocation of a set of functions (purposeful actions) of the system and its components aimed at achieving a specific goal.
Macroscopic representation - understanding of the system as an indivisible whole, interacting with the external environment.
The microscopic representation is based on the consideration of the system as a set of interrelated elements. It involves the disclosure of the structure of the system.
The hierarchical representation is based on the concept of a subsystem, obtained by decomposing (decomposing) a system that has system properties that should be distinguished from its element - indivisible into smaller parts (from the point of view of the problem being solved). The system can be represented as a set of subsystems of different levels, constituting a system hierarchy, which is closed from below only by elements.
The procedural representation involves the understanding of a system object as a dynamic object, characterized by a sequence of its states in time.
object knowledge is the honor of the real world, which stands out and is perceived as a whole for a long time. An object can be material or abstract, natural or artificial. An object has an infinite set of properties. But in practice, we need a limited set of properties that are important to us.
External environment - The concept of "system" arises where and when we materially or speculatively draw a closed boundary between an unlimited or some limited set of elements. Those elements with their respective mutual conditioning that fall inside form a system.
Those elements that remained outside the boundary form a set, called in systems theory "system environment" or simply "environment", or "external environment".
It follows from these considerations that it is unthinkable to consider a system without its external environment. The system forms and manifests its properties in the process of interaction with the environment, while being the leading component of this impact.
Depending on the impact on the environment and the nature of interaction with other systems, the functions of systems can be arranged in ascending rank as follows:
passive existence;
material for other systems;
maintenance of higher order systems;
opposition to other systems (survival);
absorption of other systems (expansion);
transformation of other systems and environments (active role).
Any system can be considered, on the one hand, as a subsystem of a higher order (supersystem), and on the other hand, as a supersystem of a system of a lower order (subsystem). For example, the system "production shop" is included as a subsystem in a system of a higher rank - "firm". In turn, the "firm" supersystem can be a "corporation" subsystem.
Usually, more or less independent parts of systems appear as subsystems, distinguished by certain characteristics, having relative independence, a certain degree of freedom.
Component - any part of the system that enters into certain relations with other parts (subsystems, elements).
Element with A system is a part of a system with uniquely defined properties that perform certain functions and are not subject to further division within the framework of the problem being solved (from the point of view of the researcher).
The concept of an element, a subsystem, a system is mutually transformable, a system can be considered as an element of a system of a higher order (metasystem), and an element in an in-depth analysis, as a system. The fact that any subsystem is simultaneously and relatively independent system leads to 2 aspects of the study of systems: at the macro- and micro-levels.
When studying at the macro level, the main attention is paid to the interaction of the system with the external environment. Moreover, higher-level systems can be considered as part of the external environment. With this approach, the main factors are the target function of the system (goal), the conditions for its functioning. At the same time, the elements of the system are studied from the point of view of their organization into a single whole, the impact on the functions of the system as a whole.
At the micro level, the internal characteristics of the system, the nature of the interaction of elements among themselves, their properties and operating conditions become the main ones.
Both components are combined to study the system.
2. Concepts of system structure. Links and their types.
The structure of the system is understood as a stable set of relations that remains unchanged for a long time, at least during the observation interval. The structure of the system is ahead of a certain level of complexity in terms of the composition of relations on the set of elements of the system, or equivalently, the level of diversity of the manifestations of the object.
Links are elements that carry out direct interaction between elements (or subsystems) of the system, as well as with elements and subsystems of the environment.
Communication is one of the fundamental concepts in systems approach. The system as a whole exists precisely due to the presence of connections between its elements, i.e., in other words, the connections express the laws of the system's functioning. Relations are distinguished by the nature of the relationship as direct and reverse, and by the type of manifestation (description) as deterministic and probabilistic.
Direct connections are intended for a given functional transfer of matter, energy, information or their combinations - from one element to another in the direction of the main process.
feedback, basically, they perform informing functions, reflecting a change in the state of the system as a result of a control action on it. The discovery of the feedback principle was an outstanding event in the development of technology and had extremely important consequences. The processes of management, adaptation, self-regulation, self-organization, development are impossible without the use of feedback.
Rice. - Feedback example
With the help of feedback, the signal (information) from the output of the system (control object) is transmitted to the control body. Here, this signal, containing information about the work performed by the control object, is compared with a signal that specifies the content and amount of work (for example, a plan). In the event of a discrepancy between the actual and planned state of work, measures are taken to eliminate it.
The main feedback functions are:
counteracting what the system itself does when it goes beyond the established limits (for example, responding to quality degradation);
compensation of disturbances and maintenance of a state of stable equilibrium of the system (for example, equipment malfunctions);
synthesizing external and internal disturbances that seek to bring the system out of a state of stable equilibrium, reducing these disturbances to deviations of one or more controlled variables (for example, the development of control commands for the simultaneous appearance of a new competitor and a decrease in the quality of products);
development of control actions on the control object according to a poorly formalized law. For example, the establishment of a higher price for energy carriers causes complex changes in the activities of various organizations, changes the final results of their functioning, requires changes in the production and economic process through impacts that cannot be described using analytical expressions.
Violation of feedback in socio-economic systems for various reasons leads to serious consequences. Separate local systems lose the ability to evolve and perceive emerging new trends, long-term development and scientifically based forecasting of their activities for a long period of time, effective adaptation to constantly changing environmental conditions.
A feature of socio-economic systems is the fact that it is not always possible to clearly express the feedback, which in them, as a rule, is long, passes through a number of intermediate links, and it is difficult to see them clearly. The controlled variables themselves often do not lend themselves to a clear definition, and it is difficult to establish many restrictions on the parameters of the controlled variables. The real reasons for the controlled variables to go beyond the established limits are also not always known.
Deterministic (hard) connection, as a rule, uniquely determines the cause and effect, gives a clearly defined formula for the interaction of elements.Probabilistic (flexible) connection -Defines an implicit and indirect dependency between elements. Probability theory offers a special mathematical apparatus for the study of these relationships, called correlation analysis.
Criteria are signs by which the conformity of the functioning of the system to its purpose is assessed under given restrictions
The efficiency of the system is the ratio between the target result of functioning and the actually realized one.
Often there are restrictions on the input and output - provides a correspondence between the output of the system and the requirements for entry into the subsequent system. If the requirements are not met, the restriction does not allow it to pass through itself, that is, it works on the principle of a filter.
The state of the system is a set of essential properties that the system has at the current moment.
3. Basic properties of systems. (6 properties).
A property is understood as the side of an object (its characteristic), which determines its difference or similarity with another object, or manifests itself during interaction.
It follows from the definition of the system that the main property is the integrity or unity provided by the relationships between the components and manifested in the emergence of new properties that individual elements do not possess.
This property is called the emergence property.
Emergence - a property of systems that causes the emergence of new properties and qualities that are not inherent in individual elements of the system. It is based on the principle opposite to reductionism, which states that the whole can be studied by dividing it into parts and then, having determined the properties of the parts, determine the properties of the whole.
Integrity - each element of the system contributes to the realization of the goal of the system.
Integrity and emergence are the integrative properties of the system.
Integrity lies in the fact that each of the components provides its own pattern of functionality and goal achievement.
The presence of integrative properties is one of the most important features of the system. Integrity is manifested in the fact that the system has its own pattern of functionality, its own purpose.
organization - complex property systems, consisting in the presence of structure and functioning (behavior). The indispensable property of systems is their components, namely those structural formations that make up the whole and without which it is not possible.
Functionality- this is a manifestation of certain properties (functions) when interacting with the external environment. Here, the goal (purpose of the system) is defined as the desired end result.
Structurality - this is the ordering of the system, a certain set and arrangement of elements with links between them. There is a relationship between the function and structure of the system, as between the philosophical categories of content and form. A change in content (functions) entails a change in form (structure), but vice versa.
An important property of the system is the presence of behavior- actions, changes, functioning, etc. It is believed that this behavior of the system is associated with the environment (environment), i.e. with other systems with which it comes into contact or enters into certain relationships. The process of purposeful change in time of the state of the system is called behavior. Unlike control, when a change in the state of the system is achieved due to external influences, behavior is implemented exclusively by the system itself, based on its own goals.
Another property is the property of growth (development). Development can be seen as an integral part of behavior (and the most important).
The fundamental property of systems is stability, i.e. the ability of the system to withstand external disturbing influences. It affects the lifespan of the system. Simple systems have passive forms of stability: strength, balance, controllability, homeostasis. And for complex ones, active forms are decisive: reliability, survivability and adaptability. If the listed forms of stability of simple systems (except for strength) concern their behavior, then the determining form of stability of complex systems is mainly structural in nature.
Reliability - the property of preserving the structure of systems, despite the death of its individual elements by replacing or duplicating them, and survivability - how active suppression harmful qualities. So the reliability is more passive form than vitality.
Adaptability - the ability to change behavior or structure in order to maintain, improve or acquire new qualities in a changing environment. A prerequisite for the possibility of adaptation is the presence of feedback.
4. Classification of systems by content. Give short description each class.
classification is called the division into classes according to the most significant features. Under class is understood as a set of objects that have some features of generality. A sign (or a set of signs) is the basis (criterion) of classification.
A system can be characterized by one or more features and, accordingly, it can be placed in various classifications, each of which can be useful in choosing a research methodology. Usually the goal of classification is to limit the choice of approaches to displaying systems, to develop a description language suitable for the corresponding class.
Real Systemsare divided into natural (natural systems) and artificial (anthropogenic).
natural systems: systems of inanimate (physical, chemical) and living (biological) nature.
Artificial systems:are created by mankind for their needs or are formed as a result of purposeful efforts. artificialare divided into technical (techno-economic) and social (public).A technical system is designed and manufactured by a person for specific purposes.
TO social systemsinclude various systems of human society.
The selection of systems consisting of only technical devices is almost always conditional, since they are not capable of generating their own state. These systems act as parts of larger, including people - organizational and technical systems.
An organizational system, for the effective functioning of which an essential factor is the way of organizing the interaction of people with a technical subsystem, is calledman-machine system. Examples of man-machine systems: car - driver; aircraft - pilot; COMPUTER - user, etc.
Thus, undertechnical systemsunderstand a single constructive set of interconnected and interacting objects, intended for purposeful actions with the task of achieving a given result in the process of functioning. The distinguishing features of technical systems in comparison with an arbitrary set of objects or in comparison with individual elements are constructiveness (practical feasibility of relations between elements), orientation and interconnectedness of constituent elements and purposefulness.
In order for the system to be resistant to external influences, it must have a stable structure. The choice of structure practically determines the technical appearance of both the entire system and its subsystems and elements. The question of the appropriateness of using a particular structure should be decided on the basis of the specific purpose of the system. The structure also determines the ability of the system to redistribute functions in the event of a complete or partial withdrawal of individual elements, and, consequently, the reliability and survivability of the system for given characteristics of its elements.
Abstract systemsare the result of the reflection of reality (real systems) in the human brain. Their mood is a necessary step in ensuring effective human interaction with the outside world. Abstract (ideal) systems are objective in terms of their source of origin, since their primary source is an objectively existing reality.
Abstract systems divideon direct display systems(reflecting certain aspects of real systems)and systems of generalizing (generalizing) mapping.The former include mathematical and heuristic models, and the latter - conceptual systems(theories of methodological construction) and languages.
5. Classification of systems into 9 groups. Give a brief description of each class.
open called a system interacting with the environment. All real systems are open. When describing the structure of such systems, external communication channels are tried to be divided into input and output.
In an open system, at least 1 element has a connection with the external environment.
In a real system, the number of interconnections is enormous. Therefore, one of the researcher's tasks is to single out and include only significant links in the system. Irrelevant are discarded.
closed system- one that does not interact with the environment, or interacts with it in a strictly defined way. In the second case, there are input channels, but the impact of the environment is unchanged and fully known in advance. In this case, such impacts are attributed directly to the system, which allows us to consider it as a closed one.
Combined systemscontain open and closed subsystems. That is, one or more subsystems can be distinguished in them, interacting with the environment, and the remaining subsystems are closed.
Simple systems - do not have branched structures and consist of a small number of relationships and elements. It serves to perform the simplest functions; it is impossible to single out hierarchical levels in them. A distinctive feature is the determinism (clear certainty) of the nomenclature, the number of elements and internal and external links.
Complex - contain a large number of elements and internal connections, differ in structural diversity. Performs a complex function or a series of functions. Can be easily divided into subsystems. A system is called complex if its knowledge requires the involvement of several scientific disciplines, theories, models, as well as accounting for uncertainty.
A model is a kind of description (mathematical, verbal, etc.) of a system or subsystem that reflects a group and its property.
A system is said to be complex if, in reality, the following signs of complexity are essentially manifested:
Structural complexity
Basic concepts of relationships:
Structural
Hierarchical
Functional
Causal (causal)
Informational
Spatio-temporal
Complexity of functioning (behavior)
Complexity of behavior choice. In multi-alternative situations, the choice of behavior is determined by the purpose of the system.
Complexity of development.
It is determined by the characteristics of evolutionary or stochastic processes.
These features should be considered in conjunction. Complex systems are characterized by weak predictability, secrecy, and a variety of possible states.
big systemcalled a system that cannot be observed simultaneously from the position of one observer in time and space. That is, the spatial factor is essential for it. The number of its subsystems is very large, and the composition is heterogeneous. In the analysis and synthesis of large and complex systems, decomposition and aggregation procedures are fundamental.
For specialized systemsthe uniqueness of the appointment and the narrow specialization of the service personnel are characteristic. In universal systems, many actions are also performed on a single structure, however, the composition of functions in terms of their type and number is less homogeneous.
Automatic - uniquely respond to a limited set of external interactions. The internal organization has several equilibrium states.
Decisive - have constant criteria for distinguishing external influences and constant reactions to them.
self-organizing- have flexible criteria for distinguishing and flexible reactions to external influences. Can adapt to influences. They have signs of diffuse systems, stochastic behavior and instability of parameters and processes. Able to slightly change the structure. For example: biological organizations, collective behavior of people, etc. If it surpasses external influences in its stability, thenthese are predictive systems. That is, they can foresee the further course of events.
Transforming systems- imaginary complex systems at the highest level of complexity, not bound by the persistence of existing carriers. They can change material carriers and their structure, while maintaining their individuality.
They are called deterministicsystems for which their state is uniquely determined by the initial moment and can be predicted for any subsequent moment of time.Stochastic systems- systems in which changes are random. In this case, the initial data for prediction is not enough.
A system is called centralized if one of its parts has a dominant (central) role, which determines the functioning.
decentralizedsystems are those systems in which the components are equally significant.
In producing systems, processes for obtaining products or services are implemented. Such systems are divided into material-energy and information.
Control systems- are engaged in the organization and management of material-energy and information processes.
Service systems- support the performance of production and control systems.
6. Name the patterns of interaction between the part and the whole (2). Give a brief description of each pattern.
Progressive systematization | d > B |
Progressive factorization |
Additivity (summativity) |
The regularity of integrity/emergence is manifested in the system in the appearance of new properties in it that are absent from the elements. In order to better understand the regularity of integrity, it is necessary, first of all, to take into account its two sides:
properties of the (whole) system Qs is not a simple sum of the properties of its constituent elements (parts):
Qs ≠ ∑Qi
the properties of the system (whole) depend on the properties of its constituent elements (parts):
Qs = f(qi)
In addition to these two main aspects, it should be borne in mind that the elements combined into a system, as a rule, lose some of their properties that are inherent in them outside the system, i.e. the system, as it were, suppresses a number of properties of elements. But, on the other hand, once elements enter the system, they can acquire new properties.
Let us turn to the pattern dual in relation to the pattern of integrity. It is called physical additivity, independence, summativity, isolation. The property of physical additivity is manifested in the system, as if broken up into independent elements; then it becomes fair
Qs = ∑Qi
In this extreme case, it is no longer possible to speak of a system.
Consider intermediate options - two conjugate patterns that can be called progressive factorization - the desire of the system to a state with more and more independent elements, and progressive systematization - the desire of the system to reduce the independence of elements, i.e. to greater integrity.
Integrity - This term is often used as a synonym for integrity. However, some researchers single out this regularity as an independent one, trying to emphasize the interest not in external factors of manifestation of integrity, but in deeper causes that cause the emergence of this property, to factors that ensure the preservation of integrity.
System-forming, system-preserving factors are called integrative, among which an important role is played by the heterogeneity and inconsistency of elements (explored by most philosophers), on the one hand, and their desire to join coalitions, on the other.
7. Name the patterns of hierarchical ordering (2). Give a brief description of each pattern.
This group of regularities also characterizes the interaction of the system with its environment - with the environment (significant or essential for the system), supersystem, subordinate systems.
Communication- This regularity forms the basis for the definition of a system where the system is not isolated from other systems, it is connected by many communications with the environment, which, in turn, is a complex and heterogeneous formation containing a supersystem (a metasystem is a higher-order system that sets the requirements and limitations of the studied system), subsystems (underlying, subordinate systems), and systems of the same level as the one under consideration.
Such a complex unity with the environment is called the pattern of communication, which, in turn, easily helps to move to hierarchy as a pattern of building the whole world and any system separated from it.
Hierarchy - The laws of hierarchy or hierarchical ordering were among the first laws of systems theory that L. fon singled out and studied. Bertalanffy. It is necessary to take into account not only the external structural side of the hierarchy, but also the functional relationships between levels. For example, in biological organizations, a higher hierarchical level has a guiding effect on the lower level subordinate to it, and this effect is manifested in the fact that the subordinate members of the hierarchy acquire new properties that they did not have in an isolated state (confirmation of the position on the influence of the whole on the elements given above), and as a result of the appearance of these new properties, a new, different “image of the whole” is formed (the influence of the properties of elements on the whole). The new whole that has arisen in this way acquires the ability to perform new functions, which is the purpose of the formation of hierarchies.
The main features of hierarchical ordering are:
Direct interaction of the system with higher and lower levels. In this case, the concept of a supersystem and a subsystem appears, a goal for the general level (for high levels), a subgoal (for low and medium levels) and a means (for underlying ones)
The pattern of integrity and emergence manifests itself at each level of the hierarchy.
8. Name the patterns of systems feasibility. Give a brief description of each pattern.
The problem of system feasibility is the least explored. Let us consider some of the patterns that help to understand this problem and take it into account when determining the principles for designing and organizing the functioning of control systems.
equifinality- This pattern characterizes, as it were, the limiting capabilities of the system. L. von Bertalanffy, who proposed this term, defined equifinality as “the ability, in contrast to the equilibrium state in closed systems, completely determined by the initial conditions, ... to achieve a time-independent state that does not depend on its initial conditions and is determined solely by the parameters of the system ". In accordance with this pattern, the system can reach the required final state, which is independent of time and determined solely by the system's own characteristics under different initial conditions and in different ways. This is a form of stability with respect to initial and boundary conditions.
The law of "necessary variety" -For the first time in systems theory, W.R. Ashby. He formulated a pattern known as the law of "necessary variety". For decision-making problems, the most important is one of the consequences of this pattern, which can be simplified in the following example.
When a researcher (DM - decision maker, observer) N encounters a problem D, the solution of which is not obvious to him, then there is a certain variety of possible solutions Vd. This diversity is opposed by the diversity of thoughts of the researcher (observer) Vn. The task of the researcher is to reduce the diversity Vd - Vn to a minimum, ideally to 0.
Ashby proved a theorem on the basis of which the following conclusion is formulated: “If Vd is given constant value, then Vd - Vn can only be reduced by a corresponding increase in Vn. only variety in N can reduce the variety created in D; only diversity can destroy diversity.”
As applied to control systems, the law of “required diversity” can be formulated as follows: the diversity of the control system (control system) Vsu must be greater than (or at least equal to) the diversity of the managed object Vou:
Vsu > Vou.
The following ways of improving management with increasing complexity of production processes are possible:
an increase in Vsu, which can be achieved by increasing the number of the administrative apparatus, improving its qualifications, mechanizing and automating managerial work;
reduction of Vou, due to the establishment of clearer and more specific rules for the behavior of system components: unification, standardization, typification, the introduction of in-line production, a reduction in the range of parts, assemblies, technological equipment, etc.;
reducing the level of management requirements, i.e. reduction in the number of constantly monitored and adjustable parameters of the controlled system;
self-organization of control objects by limiting controlled parameters by creating self-regulating units (workshops, sites with a closed production cycle, with relative independence and limiting the intervention of centralized enterprise management bodies, etc.).
9. Name the patterns of development of systems (2). Give a brief description of each pattern.
IN Lately the need to take into account, when modeling systems, the principles of their change over time, is becoming more and more recognized, for understanding which the regularities considered below can help.
Historicity - Although it would seem obvious that any system cannot be unchanged, that it not only arises, functions, develops, but also dies, and everyone can easily give examples of formation, flourishing, decline (aging) and even death (death) biological and social systems, yet for specific cases of the development of organizational systems and complex technical complexes it is difficult to determine these periods. The heads of organizations and designers of technical systems do not always take into account that time is an indispensable characteristic of the system, that each system is subject to the laws of historicity, and that this pattern is as objective as integrity, hierarchical order, etc. At the same time, the pattern of historicity can be taken into account not only passively , fixing aging, but also used to prevent the "death" of the system, developing "mechanisms" for reconstruction, reorganization of the system to preserve it in a new quality.
The pattern of self-organization-Among the main features of self-organizing systems with active elements are the ability to resist entropy (entropy in this case is the degree of uncertainty, unpredictability of the state of the system and the environment) tendencies, the ability to adapt to changing conditions, transforming its structure if necessary, etc. These outwardly manifesting abilities are based on a deeper pattern based on the combination of two conflicting trends in any real developing system: on the one hand, for all phenomena, including developing, open systems, the second law of thermodynamics is valid (“second law”) , i.e. the desire to increase entropy; on the other hand, there are negentropic (opposite to entropic) tendencies underlying evolution.
Important results in understanding the patterns of self-organization have been obtained in studies that are classified as a developing science called synergetics.
10. What is synergy? What is it for? Give a brief description of the 9 main principles of the synergistic approach.
Synergetics is called interdisciplinary scientific direction, which studies the universal laws of the processes of self-organization, evolution and cooperation. Its purpose is to construct a general theory of complex systems with special properties. Unlike simple systems, complex systems have the following main characteristics:
many heterogeneous components;
activity (purposefulness) of components;
many different, parallel relationships between components;
semiotic (weakly formalizable) nature of relationships;
cooperative behavior of components;
openness;
distribution;
dynamism, learning ability, evolutionary potential;
uncertainty of environment parameters.
A special place in synergetics is occupied by the questions of spontaneous formation of ordered structures different nature in interaction processes when the initial systems are in unstable states. Following the scientist I.Prigozhin, it can be briefly described as a "complex of sciences about emerging systems."
According to synergetic models, the evolution of a system is reduced to a sequence of nonequilibrium phase transitions. The principle of development is formulated as a successive passage of critical areas (points of bifurcations (bifurcations, ramifications)). Near the bifurcation points, there is a sharp increase in fluctuation (from Latin fluctuatio - fluctuation, deviation). The choice of development after the bifurcation is determined at the moment of instability. Therefore, the bifurcation zone is characterized by fundamental unpredictability - it is not known whether the further development of the system will become chaotic or a new, more ordered structure will be born. Here the role of uncertainty sharply increases: randomness at the entrance to a non-equilibrium situation can have catastrophic consequences at the exit. At the same time, the very possibility of spontaneous emergence of order from chaos is the most important moment of the process of self-organization in a complex system.
The main principles of the synergetic approach in modern science are as follows:
Complementarity principle of N. Bohr.In complex systems, there is a need to combine different models and methods of description that previously seemed incompatible, but now complementary to each other.
The principle of spontaneous emergence by I. Prigogine. In complex systems, special critical states are possible, when the slightest fluctuations can suddenly lead to the emergence of new structures that are completely different from the usual ones (in particular, this can lead to catastrophic consequences - “snowball” or epidemic effects).
Principle of incompatibility L. Zadeh. With an increase in the complexity of the system, the possibility of its accurate description decreases up to a certain threshold, beyond which the accuracy and relevance (semantic coherence) of information become incompatible, mutually exclusive characteristics.
The principle of uncertainty management.In complex systems, a transition from dealing with uncertainties to managing uncertainties is required. Various types of uncertainty should be deliberately introduced into the model of the system under study, since they serve as a factor that favors innovation (system mutations).
Principle of ignorance. Knowledge about complex systems is fundamentally incomplete, inaccurate and contradictory: it is usually formed not on the basis of logically rigorous concepts and judgments, but on the basis of individual opinions and collective ideas. Therefore, modeling of partial knowledge and ignorance plays an important role in such systems.
Conformity principle. The language for describing a complex system must correspond to the nature of the information available about it (the level of knowledge or uncertainty). Exact logical-mathematical, syntactic models are not a universal language; non-strict, approximate, semiotic models and informal methods are also important. One and the same object can be described by a family of languages of different rigidity.
The principle of diversity of development paths. The development of a complex system is multivariate and alternative, there is a "spectrum" of ways of its evolution. The critical turning point of the uncertainty of the future development of a complex system is associated with the presence of bifurcation zones - "branching" of possible paths for the evolution of the system.
The principle of unity and mutual transitions of order and chaos. The evolution of a complex system goes through instability; Chaos is not only destructive, but also constructive. The organizational development of complex systems involves a kind of conjunction of order and chaos.
The principle of oscillatory(pulsating) evolution. The process of evolution of a complex system is not progressive, but cyclic or wave in nature: it combines divergent (increase in diversity) and convergent (folding in diversity) trends, phases of the birth of order and maintenance of order. Open complex systems pulsate: differentiation is replaced by integration, scatter - by rapprochement, weakening of ties - by their strengthening, etc.
It is easy to understand that the listed principles of synergetic methodology can be divided into three groups: the principles of complexity (1-3), the principles of uncertainty (3-6) and the principles of evolution (7-9).
11. What are the patterns of emergence and formulation of goals (4). Give a brief description of each pattern.
The generalization of the results of research into the processes of goal formation, carried out by philosophers, psychologists, cybernetics, and the observation of the processes of substantiation and structuring of goals in specific conditions made it possible to formulate some general principles, patterns that are useful to use in practice.
The dependence of the idea of the goal and the formulation of the goal on the stage of cognition of the object (process) and on time -An analysis of the definitions of the concept of "goal" allows us to conclude that, when formulating the goal, one should strive to reflect in the formulation or in the way of presenting the goal the main contradiction: its active role in cognition, in management, and at the same time the need to make it realistic, to direct with the help of activities to obtain a certain useful result. At the same time, the formulation of the goal and the idea of the goal depend on the stage of cognition of the object, and as the idea of it develops, the goal can be reformulated.
The dependence of the goal on external and internal factors- When analyzing the causes of the emergence and formulation of goals, it should be taken into account that the goal is influenced by both external factors in relation to the system (external requirements, needs, motives, programs) and internal factors (needs, motives, programs of the system itself and its elements, performers goals); at the same time, the latter are the same factors that objectively influence the process of goal formation, as well as external factors (especially when using the concept of goal as a means of inducing action in management systems).
The manifestation in the structure of goals of the regularity of integrity -In a hierarchical structure, the regularity of integrity (emergence) manifests itself at any level of the hierarchy. In relation to the structure of goals, this means that, on the one hand, the achievement of a goal of a higher level cannot be fully ensured by the achievement of subgoals subordinate to it, although it depends on them, and, on the other hand, needs, programs (both external and internal) it is necessary to investigate at each level of structuring, and the divisions of subgoals obtained by different decision makers, due to different disclosures of uncertainty, may turn out to be different, i.e. different decision makers can offer different hierarchical structures of goals and functions, even when using the same structuring principles and techniques.
Patterns of formation of hierarchical structures of goals -Considering that the most common way to represent goals in organizational management systems are tree-like hierarchical structures ("goal trees"), let's consider the main recommendations for their formation:
the techniques used in the formation of tree-like hierarchies of goals can be reduced to two approaches: a) the formation of structures "from above" - methods of structuring, decomposition, target or goal-oriented approach, b) the formation of structures of goals "from below" - morphological, linguistic, thesaurus, terminal approach ; in practice, these approaches are usually combined;
the goals of the lower level of the hierarchy can be considered as a means to achieve the goals of the higher level, while they are also goals for the level below them;
in the hierarchical structure, as you move from the upper level to the lower one, there is a shift of the “scale” considered above from the goal-direction (goal-ideal, goal-dream) to specific goals and functions, which at the lower levels of the structure can be expressed in the form of expected results specific work, indicating the criteria for evaluating its performance, while at the upper levels of the hierarchy, the indication of criteria can be either expressed in general requirements(for example, “improve efficiency”), or is not given at all in the statement of the goal;
in order for the structure of goals to be convenient for analysis and organization of management, it is recommended to impose some requirements on it - the number of hierarchy levels and the number of components in each node should be (due to the Miller hypothesis or the Kolmogorov number) K = 5 ± 2 (human perception limit) .
And a few more important laws.
Law of Simplicity of Complex Systems- It is realized, survives, the variant of a complex system that has the least complexity is selected. The law of simplicity of complex systems is realized by nature in a number of constructive principles:
occam,
hierarchical modular construction of complex systems,
symmetry,
symmorphosis (equal strength, uniformity),
field interaction (interaction through a carrier),
extreme uncertainty (distribution functions of characteristics and parameters that have uncertain values have extreme uncertainty).
The law of finiteness of the rate of propagation of interaction- All types of interaction between systems, their parts and elements have a finite propagation speed. The speed of changing the states of the elements of the system is also limited. The author of the law is A. Einstein.
Godel's incompleteness theorem- In sufficiently rich theories (including arithmetic), there are always unprovable true expressions. Since complex systems include (implement) elementary arithmetic, deadlock situations (freezes) may occur when performing calculations in it.
The law of equivalence of options for building complex systems- As the complexity of the system grows, the proportion of options for its construction that are close to the optimal option grows.
Onsager's law maximization of the entropy decrease - If the number of possible forms of the process implementation, consistent with the laws of physics, is not unique, then the form is realized in which the entropy of the system grows most slowly. In other words, that form is realized in which the decrease in entropy or the increase in information contained in the system is maximized.
12. What is meant by the functional description of systems? Why and how is it done? Explain the general formula for the functional description of any dynamical system.
The study of any system involves the creation of a system model that allows you to analyze and predict its behavior in a certain range of conditions, solve problems of analysis and synthesis of a real system. Depending on the goals and objectives of modeling, it can be carried out at various levels of abstraction.
A model is a description of a system that reflects a certain group of its properties.
It is advisable to start the description of the system from three points of view: functional, morphological and informational.
Any object is characterized by the results of its existence, the place it occupies among other objects, the role it plays in the environment. A functional description is necessary in order to realize the importance of the system, to determine its place, to evaluate the relationship with other systems.
A functional description (functional model) should create the correct orientation in relation to the external relations of the system, its contacts with the outside world, and the directions of its possible change.
The functional description proceeds from the fact that any system performs some functions: it simply passively exists, serves as a habitat for other systems, serves systems of a higher order, serves as a means for creating more perfect systems.
As we already know, the system can be single-functional and multifunctional.
In many ways, the evaluation of the functions of the system (in the absolute sense) depends on the point of view of the one who evaluates it (or the system that evaluates it).
The functioning of the system can be described by a numerical functional depending on the functions that describe internal processes system, or qualitative functionality (ordering in terms of "better", "worse", "more", "less", etc.)
The functional that quantitatively or qualitatively describes the activity of the system is called the efficiency functional.
The functional organization can be described as:
algorithmically,
analytically,
graphically,
tabular,
through timing diagrams of functioning,
verbally (wordly).
The description must correspond to the concept of development of systems of a certain class and meet certain requirements:
should be open and allow the possibility of expanding (narrowing) the range of functions implemented by the system;
provide for the possibility of moving from one level of consideration to another, i.e. ensure the construction of virtual models of systems of any level.
When describing a system, we will consider it as a structure into which something (substance, energy, information) is introduced at certain points in time, and from which something is output at certain points in time.
In the most general form, the functional description of a system in any dynamic system is represented by a seven:
Sf = (T, x, C, Q, y, φ, η),
where T is the set of time points, x is the set of instantaneous values of input actions, С = (c: T → x) is the set of admissible input actions; Q - set of states; y - set of output values; Y = (u: T → y) - set of output values; φ = (T×T×T×c → Q) - state transition function; η:T×Q → y - output mapping; c - segment of the input action; u - segment of the output value.
Such a description of the system covers a wide range of properties.
The disadvantage of this description is that it is not constructive: the difficulty of interpretation and practical application. A functional description should reflect such characteristics of complex and poorly known systems as parameters, processes, hierarchy.
Let us assume that the system S performs N functions ψ1, ψ2, ..., ψs, ..., ψN, depending on n processes F1, F2, ..., Fi, ..., Fn. Efficiency s-th functions
Es = Es(ψs) = E(F1, F2, ..., Fi, ..., Fn) = Es((Fi)), i = 1...n, s = 1...N.
The overall efficiency of the system is the vector-functional E = (Es). The effectiveness of the system depends on a huge number of internal and external factors. It is extremely difficult to represent this dependence in an explicit form, and the practical value of such a representation is negligible due to the multidimensionality and multiply connectedness. A rational way to form a functional description is to use such a multi-level hierarchy of descriptions, in which the description of a higher level will depend on the generalized and factorized variables of the lower level.
The hierarchy is created by level factorization of processes (Fi) using generalized parameters (Qi), which are functionals (Fi). It is assumed that the number of parameters is much less than the number of variables on which the processes depend. This way of description allows building a bridge between the properties of the elements interacting with the environment (subsystems of the lower level) and the efficiency of the system.
Processes (Fi(1)) can be detected at the output of the system. These are the processes of interaction with the environment. We will call them processes of the first level and assume that they are defined:
first level system parameters - Q1(1), Q2(1), ..., Qj(1), ..., Qm(1);
active opposing parameters of the environment, directly directed against the system to reduce its effectiveness - b1, b2, ..., bk, ..., bK;
neutral (random environment parameters) c1, c2, ..., cl, ..., cL;
favorable environment parameters d1, d2, ..., dp, ..., dP.
The environment has direct contact with subsystems of lower levels, acting through them on subsystems of a higher level of the hierarchy, so that Fi* = Fi*((bk), (cl), (dp)). By constructing a hierarchy (parameters of the β-th level - processes of the (β-1)-th level - parameters of the (β-1)-th level), one can associate the properties of the environment with the efficiency of the system.
The system parameters (Qj) can change when the environment changes, they depend on the processes in the system and are written as state functionals Qj1(t).
The proper functional space of the system W is the space whose points are all possible states of the system, determined by the set of parameters up to level b:
Q = (Q(1), Q(2), ... Q(β)).
The state can be kept constant for some time interval T.
Processes (Fi(2)) cannot be detected at system output. These are the processes of the second level, which depend on the parameters Q(2) of the subsystems of the system (parameters of the second level). Etc.
The following description hierarchy is formed: efficiency (a finite set of functionals) - first-level processes (functions) - first-level parameters (functionals) - second-level processes (functions) - second-level parameters (functionals), etc. At some level, our knowledge of the functional properties of the system is exhausted, and the hierarchy breaks off. A break can occur at different levels for different parameters (processes), both on the process and on the parameter.
The external characteristics of the system are determined by the top level of the hierarchy, so it is often possible to confine ourselves to the description of the form ((Эi),(ψS), (Fi(1)), (Qj(1)), (bk), (cl), (dp)). The number of hierarchy levels depends on the required accuracy of input processes representation.
13. Graphic methods functional description of systems. Tree of system functions.
The method of generalized analytical functional description of systems was considered above. Very often, in the analysis and synthesis of systems, a graphical description is used, the varieties of which are:
system function tree,
functional modeling standard IDEF0.
All functions implemented by a complex system can be conditionally divided into three groups:
objective function;
basic functions of the system;
additional features of the system.
The target function of the system corresponds to its main functional purpose, i.e. target (main) function - reflects the purpose, essence and meaning of the existence of the system.
The main functions reflect the orientation of the system and represent a set of macro functions implemented by the system. These functions determine the existence of a system of a certain class. Basic functions - provide conditions for the implementation of the target function (reception, transmission, acquisition, storage, issuance).
Additional (service) functions expand the functionality of the system, the scope of their application and improve the quality of the system. Additional functions - provide conditions for the implementation of basic functions (connection (breeding, direction, guarantee)).
The description of an object in the language of functions is represented as a graph.
The wording of the function inside the vertices should include 2 words: the verb and the noun "Do what".
The system functions tree represents a decomposition of the system functions and is formed for the purpose of a detailed study of the system functionality and analysis of the set of functions implemented at different levels of the system hierarchy. On the basis of the tree of system functions, the system structure is formed on the basis of functional modules. In the future, the structure based on such modules is covered by constructive modules (for technical systems) or organizational modules (for organizational and technical systems). Thus, the stage of forming the function tree is one of the most important not only in the analysis, but also in the synthesis of the system structure. Errors at this stage lead to the creation of "disabled systems" that are not capable of fully functional adaptation with other systems, the user and the environment.
The initial data for the formation of the function tree are the main and additional functions of the system.
The formation of a function tree represents the process of decomposition of the objective function and the set of basic and additional functions into more elementary functions implemented at subsequent levels of decomposition.
At the same time, each of the functions of a specifically taken i-th level can be considered as a macro-function in relation to the functions that implement it at the (i + 1)-th level, and as elementary function in relation to the corresponding function of the upper (i-1)-th level.
The description of system functions using IDEF0 notation is based on the same decomposition principles, but is presented not as a tree, but as a set of diagrams.
14. Graphical methods of functional description of systems. IDEF0 methodology. The syntax of the language.
The objects of modeling are systems.
The description of the IDEF0 model is built in the form of a hierarchical pyramid, at the top of which is the most general description of the system, and the bottom is a set of more detailed descriptions.
IDEF0 methodology is built on the following principles:
Graphic description of the simulated processes. Graphical language of Blocks and Arcs IDEF0 Diagrams displays operations or functions in the form of Blocks, and the interaction between the inputs/outputs of operations entering or exiting the Block, Arcs.
Conciseness. Due to the use of a graphic language for describing processes, on the one hand, the accuracy of the description is achieved, and on the other, brevity.
The need to comply with the rules and the accuracy of information transfer. When modeling IDEF0, you must adhere to the following rules:
There must be at least 3 and no more than 6 functional Blocks on the Diagram.
Diagrams should display information within the context defined by purpose and point of view.
Diagrams must have a coherent interface when Block numbers, Arcs and ICOM codes have the same structure.
Uniqueness of block function names and arc names.
Clear definition of the role of data and separation of inputs and controls.
Notes for Arcs and Block function names should be short and concise.
Each Function Block requires at least one Control Arc.
A model is always built for a specific purpose and from a specific point of view.
In the process of modeling, it is very important to clearly define the direction of the development of the model - its context, point of view and purpose.
The context of the model outlines the boundaries of the system being modeled and describes its relationship with the external environment.
It must be remembered that one model represents one point of view. Multiple models are used to model a system from multiple perspectives.
The purpose reflects the reason for creating the model and determines its purpose. At the same time, all interactions in the model are considered precisely from the point of view of achieving the set goal.
Within the framework of the IDEF0 methodology, the system model is described using Graphic IDEF0 Diagrams and refined through the use of FEO, Text and Glossary Diagrams. At the same time, the model includes a series of interconnected Diagrams that divide a complex system into its component parts. Diagrams of a higher level (A-0, A0) - are the most general description of the system, presented in the form of separate Blocks. The decomposition of these Blocks makes it possible to achieve the required level of detail in the description of the system.
The development of IDEF0 Diagrams begins with the construction of the highest level of the hierarchy (A-0) - one Block and interface Arcs that describe the external links of the system under consideration. The name of the function, written in Block 0, is the target function of the system from the accepted point of view and the purpose of building the model.
In further modeling, Block 0 is decomposed on Diagram A0, where the objective function is refined using several Blocks, the interaction between which is described using Arcs. In turn, the functional Blocks in Diagram A0 can also be decomposed for a more detailed representation.
As a result, the names of functional Blocks and interface Arcs that describe the interaction of all Blocks presented in the Diagrams form a hierarchical mutually consistent model.
Although the top of the model is the A-0 Diagram, the real “working vertex or structure” is the A0 Diagram, since it is a refined expression of the model's point of view. Its content indicates what will be considered further, limiting the subsequent levels within the scope of the project goal. The lower levels specify the content of the functional Blocks, detailing them, but without expanding the boundaries of the model.
15. IDEF0 methodology. Doug concept. Five types of relationships between blocks. Block decomposition principle.
Blocks represent functions or actions of a system. Their actions are written verb + action object + object
for example, "develop a schedule of work."
Arcs display information or material objects that are necessary to perform a function or appear as a result of execution. The role of an object can be: Documents, physical materials, tools, machines, information, organizations and even subsystems. The connection point of the arc with the block determines the interface type. Remarks to the arc are formulated as a turnover of a noun, answering the question "what". Blocks are arranged on the diagram according to the degree of the author, depending on the degree of the author. The dominant block is the block whose execution affects the control for the maximum number of blocks. The dominant block is located in the upper left corner, the least important - in the lower right.
Important!
The location of the blocks does not set the time dependence of the operation!
See fig. one
Relationship management.
Input relationship. (conveyor)
Management feedback. The output of the first function controls the input of the second, which in turn affects the operation of the first.
Input feedback.
Relationship output - mechanism. A rare type of communication used in preparatory operations.
Example: create an idef model for the control department to evaluate the effectiveness of the management and functioning of the library. see Figure 2. Block A0, reflecting the objective function. Then, in Figure 3, the diagram A0 is decomposed. If necessary, each of the blocks must be decomposed.
Decomposition - scientific method, which uses the structure of the problem and allows you to replace the solution of one large problem with the solution of a series of smaller problems.
16. Morphological description and modeling of systems. Description of the structure of the system and the relationships between elements.
morphological description should give an idea of the structure of the system (morphology is the science of form, structure). Depth of description, level of detail, i.e. the definition of which components of the system will be considered as elementary (elements) is determined by the purpose of the description of the system. The morphological description is hierarchical. The morphology configuration is given at as many levels as are required to represent the basic properties of the system.
Goals structural analysis are:
development of rules for the symbolic display of systems;
assessment of the quality of the system structure;
study of the structural properties of the system as a whole and its subsystems;
development of a conclusion on the optimality of the structure of the system and recommendations for its further improvement.
In the structural approach, two stages can be distinguished: determination of the composition of the system, i.e. a complete enumeration of its subsystems, elements, and clarification of the relationships between them.
The study of the system morphology begins with the elemental composition. He might be:
homogeneous (elements of the same type);
heterogeneous (various elements);
mixed.
Uniformity does not mean complete identity and determines only the proximity of the main properties.
Homogeneity, as a rule, is accompanied by redundancy and the presence of hidden (potential) opportunities, additional reserves.
Heterogeneous elements are specialized, they are economical and can be effective in a narrow range of environmental conditions, but quickly lose effectiveness outside this range.
Sometimes the elemental composition cannot be determined - indefinite.
An important feature of morphology is the purpose (properties) of elements. Distinguish elements:
informational;
energy;
real.
It should be remembered that such a division is conditional and reflects only the prevailing properties of the element. In the general case, the transfer of information is not possible without energy, the transfer of energy is not possible without information.
Information elements are intended for receiving, storing (storing), converting and transmitting information. The transformation may consist in changing the type of energy that carries information, in changing the method of encoding (representing in some sign form) information, in compressing information by reducing redundancy, decision making, etc.
There are reversible and irreversible transformations of information.
Reversible are not associated with the loss (or creation of new) information. Accumulation (memorization) is reversible if there is no loss of information during the storage time.
Energy transformation consists in changing the parameters of the energy flow. The input energy flow can come from outside, or from other elements of the system. The output energy flow is directed to other systems or to the environment. The process of energy conversion naturally needs information.
The process of transformation of a substance can be mechanical (for example, stamping), chemical, physical (for example, cutting), biological. In complex systems, the transformation of matter is of a mixed nature.
IN general case, it should be borne in mind that any processes, one way or another, lead to the transformation of matter, energy and information.
The morphological properties of the system essentially depend on the nature of the links between the elements. The concept of connection is included in any definition of a system. It simultaneously characterizes both the structure (statics) and the functioning (dynamics) of the system. Links ensure the emergence and preservation of the structure and properties of the system. Allocate informational, material and energy connections, defining them in the same sense in which the elements were defined.
The nature of the connection is determined by the specific weight of the corresponding component (or objective function).
Communication is characterized by:
direction,
force,
view.
According to the first two signs, connections are divided into directed and non-directed, strong and weak, and by nature - subordination, generation (genetic), equal and control connections.
Some of these links can be broken down in even more detail. For example, links of subordination on the links “genus-species”, “part-whole”; connections of generation - "cause-effect".
They can also be divided according to the place of application (internal - external), according to the direction of the processes (direct, reverse, neutral).
Direct connections are intended for the transfer of matter, energy, information or their combinations from one element to another in accordance with the sequence of functions performed.
The quality of a connection is determined by its throughput and reliability.
A very important role, as we already know, is played by feedback - they are the main self-regulation and development of systems, their adaptation to changing conditions of existence. They mainly serve for process control and information feedback is the most common.
Neutral connections are not related to the functional activity of the system, they are unpredictable and random. However, neutral links can play a certain role in the adaptation of the system, serve as an initial resource for the formation of direct and reverse links, and be a reserve.
The morphological description may include indications of the presence and type of connection, contain general characteristics connections or their qualitative and quantitative assessments.
Structural properties of systems are determined by the nature and stability of relationships between elements. According to the nature of the relationship between the elements of the structure, they are divided into:
multi-connected,
hierarchical,
mixed.
The most stable are deterministic structures in which relations are either constant or change in time according to deterministic laws. Probabilistic structures change in time according to probabilistic laws. Chaotic structures are characterized by the absence of restrictions, the elements in them come into contact in accordance with individual properties. Classification is made according to the dominant feature.
The structure plays a major role in the formation of new properties of the system, different from the properties of its components, in maintaining the integrity and stability of its properties in relation to changes in the elements of the system within certain limits.
Important structural components are relations of coordination and subordination.
Coordination expresses the ordering of the elements of the system "horizontally". Here we are talking about the interaction of components of the same level of organization.
Subordination - "vertical" ordering of subordination and subordination of components. Here we are talking about the interaction of components of different levels of the hierarchy.
Hierarchy (hiezosazche - sacred power, Greek) is the arrangement of the parts of the whole in order from the highest to the lowest. The term "hierarchy" (multi-stage) defines the ordering of system components in order of importance. Between the levels of the hierarchy of the structure, there can be relationships of strict subordination of the components of the lower level to one of the components of the higher level, i.e. tree-order relationships. Such hierarchies are called strong or tree-type hierarchies.
However, tree-like relationships do not have to exist between the levels of the hierarchical structure. Relationships can also occur within the same hierarchy level. An underlying component may be subordinate to several components of a higher level - these are hierarchical structures with weak links.
Hierarchical structures are characterized by the presence of managerial and executive components. There may be components that are both control and executive.
There are strictly and non-strictly hierarchical structures.
The system of a strict hierarchical structure has the following features:
the system has one main control component, which has at least two links;
there are executive components, each of which has only one connection with the higher-level component;
communication exists only between components belonging to two neighboring levels, while the components of the lower level are associated with only one component of the higher level, and each component of the higher level is associated with at least two components of the lower one. Fig.1
Rice. 2.
Figure 1 shows a graph of a strictly hierarchical structure, Figure 2 shows a graph of a non-strict hierarchical structure. Both structures have three levels.
So in Fig. 1, the element of the 1st level of the hierarchy can represent the rector of the university, the elements of the 2nd level - vice-rectors, the 3rd level - deans, the remaining elements (4th level, not shown in the figure) will represent the heads of departments. It is clear that all the elements and connections of the presented structure are not equal.
As a rule, the presence of a hierarchy is a sign of a high level of organization of the structure, although there may be non-hierarchical highly organized systems.
Functionally, hierarchical structures are more economical.
For non-hierarchical structures, there are no components that are only control or only executive. Any component interacts with more than one component.
Rice. 3 - Graph of the multiply connected structure of the system
Rice. 4 - Graph of the cellular structure of the system
Mixed structures are various combinations of hierarchical and non-hierarchical structures.
Let's introduce the concept of leadership.
A leading subsystem is one that satisfies the following requirements:
the subsystem does not have a deterministic interaction with any subsystem;
the subsystem is control (with direct or indirect interaction) in relation to the part (the largest number of subsystems);
a subsystem is either not controlled (subordinate) or controlled by the smallest (compared to others) number of subsystems.
There can be more than one leading subsystem, with several leading subsystems, the main leading subsystem is possible. The subsystem of the highest level of the hierarchical structure must simultaneously be the main leading one, but if this is not the case, then the proposed hierarchical structure is either unstable or does not correspond to the true structure of the system.
Mixed structures are various combinations of hierarchical and non-hierarchical structures. The stability of the structure is characterized by the time of its change. A struct can be changed without class conversion or by converting one class to another. In particular, the emergence of a leader in a non-hierarchical structure can lead to its transformation into a hierarchical one, and the emergence of a leader in a hierarchical structure can lead to the establishment of a limiting and then deterministic connection between the leading subsystem and the top-level subsystem. As a result, the top-level subsystem is replaced by the leading subsystem, or merged with it, or the hierarchical structure is transformed into a non-hierarchical (mixed) one.
Equilibrium structures are called non-hierarchical structures without leaders. Most often, multiply connected structures are equilibrium. Equilibrium does not mean the component-by-component identity of metabolism, it is only about the degree of influence on decision-making.
A feature of hierarchical structures is the absence of horizontal links between elements. In this sense, these structures are abstract constructions, since in reality it is difficult to find a production or any other operating system with missing horizontal connections.
In the morphological description of a system, its compositional properties are of great importance. The compositional properties of systems are determined by the way elements are combined into subsystems. We will distinguish subsystems:
effector (capable of transforming the impact and acting with matter or energy on other subsystems and systems, including the environment),
receptor (capable of converting external influences into information signals, transmitting and transferring information)
reflexive (capable of reproducing processes within themselves at the information level, generating information).
The composition of systems that do not contain (up to the elemental level) subsystems with pronounced properties is called weak. The composition of systems containing elements with pronounced functions is called, respectively, with effector, receptor or reflexive subsystems; combinations are possible. The composition of systems that include subsystems of all three types will be called complete. Elements of the system (i.e., subsystems into which morphological analysis does not extend) can have effector, receptor, or reflex properties, as well as their combinations.
In set-theoretic language, a morphological description is a quadruple:
SM = (S, V, d, K),
where S=(Si)i is the set of elements and their properties (in this case, an element is understood as a subsystem, into which the morphological description does not penetrate); V =(Vj)j - set of links; δ - structure; K - composition.
We consider all sets to be finite.
We will distinguish in S:
Composition:
homogeneous,
heterogeneous,
mixed (a large number of homogeneous elements with a certain number of heterogeneous),
uncertain.
Element properties:
information,
energy,
information and energy,
material and energy,
indefinite (neutral).
We will distinguish in the set V:
Purpose of links:
information,
real,
energy.
The nature of the connections:
straight,
reverse,
neutral.
We will distinguish in d:
Structural stability:
deterministic
probabilistic
chaotic.
Buildings:
hierarchical,
multi-connected,
mixed,
transforming.
We will distinguish in the set K:
Compositions:
weak,
with effector subsystems,
with receptor subsystems,
with reflective subsystems,
full,
indefinite.
The morphological description, as well as the functional one, is built according to the hierarchical (multi-level) principle by sequential decomposition of subsystems. The levels of decomposition of the system, the levels of the hierarchy of the functional and morphological description must match. The morphological description can be performed by sequential dissection of the system. This is convenient if the connections between subsystems of the same hierarchy level are not too complex. The most productive (for practical problems) are descriptions with a single articulation or with a small number of them. Each element of the structure can, in turn, be described functionally and informationally. The morphological properties of the structure are characterized by the time it takes to establish a connection between the elements and the throughput of the connection. It can be proved that the set of structure elements forms a normal metric space. Therefore, it is possible to define a metric (the concept of distance) in it. To solve some problems, it is expedient to introduce a metric in the structural space.
17. Methods for describing structures in morphological description. Structure graphs.
Block diagrams- The formation of the structure is part of the solution of the general problem of describing the system. The structure reveals the general configuration of the system, and does not define the system as a whole.
If we depict the system as a set of blocks that carry out some functional transformations, and connections between them, then we get a block diagram that describes the structure of the system in a generalized form. A block is usually understood, especially in technical systems, functionally complete and designed as a separate whole device. Division into blocks can be carried out on the basis of the required degree of detail in the description of the structure, the visibility of the display in it of the features of the functioning processes inherent in the system. In addition to functional ones, logical blocks can be included in the block diagram, allowing you to change the nature of the operation depending on whether some predetermined conditions are met or not.
Structural diagrams are visual and contain information about a large number of structural properties of the system. They are easy to refine and concretize, during which it is not necessary to change the entire scheme, but it is enough to replace its individual elements with block diagrams that include not one, as before, but several interacting blocks.
However, a block diagram is not yet a structure model. It is difficult to formalize and is rather a natural bridge facilitating the transition from a meaningful description of the system to a mathematical description than a real tool for analyzing and synthesizing structures. Rice. - Block diagram example
Counts - The relations between the elements of the structure can be represented by a corresponding graph, which makes it possible to formalize the process of studying time-invariant properties of systems and to use the well-developed mathematical apparatus of graph theory.
Definition. A graph is a triple G=(M, R, P), where M is a set of vertices, R is a set of edges (or graph arcs), P is the incidence predicate of graph vertices and edges. P(x, y, r) = 1 means that vertices x,y
∈
M are incident (connected, lie on) an edge of the graph r∈
R.
To make it easier to work with a graph, its vertices are usually numbered. A graph with numbered vertices is called marked.
Each edge of the graph connects two vertices, which in this case are called adjacent. If the graph is marked, then the edge is given by the pair (i,j), where i and j are the numbers of adjacent vertices. Obviously, the edge (i,j) is incident to the vertices i and j , and vice versa.
If all the edges of the graph are given by ordered pairs (i, j), in which the order of the adjacent vertices matters, then the graph is called directed. An undirected graph contains no directed edges. In a partially directed graph, not all edges are directed.
Geometrically, graphs are depicted as diagrams, on which vertices are displayed as points (circles, rectangles), and edges as segments connecting adjacent vertices. An oriented edge is defined by a segment with an arrow.
The use of diagrams is so widespread that when people talk about a graph, they usually think of a diagram of a graph.
If the edges of the graph have some numerical characteristics connections, then such graphs are called weighted. In this case, the incidence matrix contains the weights of the corresponding links, the sign before the number determines the direction of the edge.
An important characteristic of a structural graph is the number of possible paths that can be taken from one vertex to another. The more such paths, the more perfect the structure, but the more redundant it is. Redundancy ensures the reliability of the structure. For example, the destruction of 90% of the neural connections of the brain is not felt and does not affect behavior. There can also be useless redundancy, which is represented as loops in the structural graph.
18. Structure of system analysis. Basic decision cycle. Function tree.
The general approach to problem solving can be represented as a cycle.
At the same time, in the process of functioning of a real system, the problem of practice is revealed as a discrepancy between the existing state of affairs and the required one. To solve the problem, a systematic study (decomposition, analysis and synthesis) of the system is carried out, which removes the problem. During the synthesis, the analyzed and synthesized systems are evaluated. The implementation of the synthesized system in the form of the proposed physical system allows us to assess the degree of removal of the problem of practice and make a decision on the functioning of the modernized (new) real system.
With this view, another aspect of the definition of a system becomes apparent: the system is a means of solving problems.
The main tasks of system analysis can be represented as a three-level tree of functions.
At the stage of decomposition, which provides a general representation of the system, the following are carried out:
Definition and decomposition of the general goal of the study and the main function of the system as a restriction of the trajectory in the state space of the system or in the area of admissible situations. Most often, decomposition is carried out by constructing a tree of goals and a tree of functions.
Isolation of the system from the environment (separation into a system / "non-system") according to the criterion of participation of each element under consideration in the process, leading to a result based on the consideration of the system as an integral part of the supersystem.
Description of influencing factors.
Description of development trends, uncertainties of various kinds.
Description of the system as a "black box".
Functional (by functions), component (by type of elements) and structural (by type of relations between elements) decomposition of the system.
Depth of decomposition is limited. The decomposition must stop if it is necessary to change the level of abstraction - to present the element as a subsystem. If during decomposition it turns out that the model begins to describe the internal algorithm of the element’s functioning instead of the law of its functioning in the form of a “black box”, then in this case the level of abstraction has changed. This means going beyond the goal of studying the system and, therefore, causes the decomposition to stop.
In automated methods, the decomposition of the model to a depth of 5-6 levels is typical. One of the subsystems is usually decomposed to such a depth. Features that require this level of detail are often very important and detailed description gives the key to the secrets of how the whole system works.
It has been proven in general systems theory that most systems can be decomposed into basic representations of subsystems. These include: serial (cascade) connection of elements, parallel connection of elements, connection using feedback.
The problem of decomposition is that in complex systems there is no one-to-one correspondence between the law of functioning of subsystems and the algorithm, its implementation. Therefore, the formation of several options (or one option, if the system is displayed as a hierarchical structure) of the system decomposition is carried out.
Let's look at some of the most commonly used decomposition strategies.
Functional decomposition. Decomposition is based on the analysis of system functions. This raises the question of what the system does, regardless of how it works. The division into functional subsystems is based on the commonality of functions performed by groups of elements.
Decomposition by life cycle. A sign of the allocation of subsystems is a change in the law of functioning of subsystems at different stages of the cycle of existence of the system "from birth to death". It is recommended to apply this strategy when the goal of the system is to optimize processes and when it is possible to determine the successive stages of converting inputs to outputs.
Decomposition by physical process. A sign of subsystem selection is the steps of the subsystem functioning algorithm execution, the stages of changing states. While this strategy is useful in describing existing processes, it can often result in a system description that is too coherent and does not take full account of the limitations that functions impose on one another. In this case, the control sequence may be hidden. This strategy should be applied only if the purpose of the model is to describe the physical process as such.
Decomposition by subsystems (structural decomposition). A sign of subsystem allocation is a strong connection between elements according to one of the types of relations (connections) existing in the system (informational, logical, hierarchical, energy, etc.). The strength of communication, for example, according to information, can be estimated by the coefficient of information interconnection of subsystems k = N / N0, where N is the number of mutually used information arrays in subsystems, N0 is the total number of information arrays. To describe the entire system, a composite model must be built that combines all the individual models. It is recommended to use decomposition into subsystems only when such division into the main parts of the system does not change. The instability of the boundaries of subsystems will quickly devalue both individual models and their combination.
At the analysis stage, which provides the formation of a detailed representation of the system, the following are carried out:
Functional and structural analysis of the existing system, which allows to formulate requirements for the system being created. It includes clarification of the composition and laws of the functioning of elements, algorithms of functioning and mutual influences of subsystems, separation of controlled and uncontrolled characteristics, setting the state space Z, setting parametric space T, in which the behavior of the system is specified, the analysis of the integrity of the system, the formulation of requirements for the system being created.
Morphological analysis - analysis of the relationship of components.
Genetic analysis - analysis of the background, the reasons for the development of the situation, existing trends, making forecasts.
Analysis of analogues.
Analysis of efficiency (in terms of effectiveness, resource intensity, efficiency). It includes the choice of a measurement scale, the formation of performance indicators, the justification and formation of performance criteria, the direct evaluation and analysis of the obtained assessments.
Formation of requirements for the system being created, including the choice of evaluation criteria and restrictions.
Stage of system synthesis, problem solving, is presented as a simplified functional diagram in the figure. At this stage, the following are carried out:
Development of a model of the required system (selection of a mathematical apparatus, modeling, evaluation of the model according to the criteria of adequacy, simplicity, correspondence between accuracy and complexity, balance of errors, multivariate implementations, block construction).
Synthesis of alternative structures of the system that removes the problem.
Synthesis of the parameters of the system that removes the problem.
Evaluation of variants of the synthesized system (substantiation of the evaluation scheme, implementation of the model, evaluation experiment, processing of evaluation results, analysis of results, selection of the best variant).
Rice. - Simplified functional diagram of the stage of synthesis of the system solving the problem
An assessment of the degree of removal of the problem is carried out at the completion of the system analysis.
The most difficult to perform are the stages of decomposition and analysis. This is due to the high degree of uncertainty that needs to be overcome in the course of the study.
19. 9 stages of system representation formation.
Stage 1. Identification of the main functions (properties, goals, purpose) of the system. Formation (selection) of the main subject concepts used in the system. At this stage, it is about understanding the main outputs in the system. This is the best place to start your research. The type of output must be determined: material, energy, information, they must be attributed to some physical or other concepts (production output - products (what?), Control system output - command information (for what? in what form?), output of an automated information system - information (about what?), etc.).
Stage 2. Identification of the main functions and parts (modules) in the system. Understanding the unity of these parts within the system. At this stage, the first acquaintance with the internal content of the system takes place, it is revealed what large parts it consists of and what role each part plays in the system. This is the stage of obtaining primary information about the structure and nature of the main links. Such information should be presented and studied using structural or object-oriented methods of system analysis, where, for example, the presence of a predominantly serial or parallel nature of the connection of parts, mutual or predominantly unilateral direction of influences between parts, etc. Already at this stage, attention should be paid to the so-called system-forming factors, i.e. on those connections, interdependencies that make the system a system.
Stage 3. Identification of the main processes in the system, their role, conditions for implementation; identification of staging, jumps, changes of states in functioning; in systems with control - the allocation of the main control factors. Here, the dynamics of the most important changes in the system, the course of events are studied, state parameters are introduced, the factors influencing these parameters that ensure the course of processes, as well as the conditions for the beginning and end of processes, are considered. It is determined whether the processes are manageable and whether they contribute to the implementation of the system's main functions. For controlled systems, the main control actions, their type, source and degree of influence on the system are clarified.
Stage 4. Identification of the main elements of the "non-system" with which the system under study is associated. Identification of the nature of these relationships. At this stage, a number of individual problems are solved. The main external influences on the system (inputs) are investigated. Their type (material, energy, information), the degree of influence on the system, and the main characteristics are determined. The boundaries of what is considered a system are fixed, the elements of the “non-system” are determined, to which the main output effects are directed. Here it is also useful to trace the evolution of the system, the path of its formation. Often this is what leads to an understanding of the structure and features of the functioning of the system. In general, this stage allows you to better understand the main functions of the system, its dependence and vulnerability or relative independence in the external environment.
Stage 5. Identification of uncertainties and accidents in the situation of their determining influence on the system (for stochastic systems).
Stage 6. Identification of a branched structure, hierarchy, formation of ideas about the system as a set of modules connected by inputs and outputs.
Stage 6 ends with the formation of general ideas about the system. As a rule, this is enough if we are talking about an object with which we will not work directly. If we are talking about a system that needs to be studied for its in-depth study, improvement, management, then we will have to go further along the spiral path of in-depth study of the system.
Formation of a detailed representation of the system
Stage 7. Identification of all elements and relationships important for the purposes of the review. Their assignment to the hierarchy structure in the system. Ranking of elements and links according to their importance.
Stages 6 and 7 are closely related to each other, so it is useful to discuss them together. Stage 6 is the limit of cognition "inside" a rather complex system for a person who operates it entirely. More in-depth knowledge of the system (stage 7) will have only a specialist responsible for its individual parts. For a not too complex object, the level of stage 7 - knowledge of the whole system - is achievable for one person. Thus, although the essence of stages 6 and 7 is the same, but in the first of them we are limited to the reasonable amount of information that is available to one researcher.
With in-depth detailing, it is important to single out exactly the elements (modules) and connections that are essential for consideration, discarding everything that is not of interest for the purposes of the study. Cognition of the system does not always mean only separating the essential from the non-essential, but also focusing attention on the more essential. Detailing should also affect the connection of the system with the “non-system”, already considered in stage 4. At stage 7, the set of external relations is considered clarified to such an extent that one can speak of a thorough knowledge of the system.
Stages 6 and 7 summarize the overall, integral study of the system. Further stages already consider only its individual aspects. Therefore, it is important to once again pay attention to the system-forming factors, to the role of each element and each connection, to understanding why they are exactly like that or should be exactly like that in terms of the unity of the system.
Stage 8. Accounting for changes and uncertainties in the system. Here we study a slow, usually undesirable change in the properties of the system, which is commonly called "aging", as well as the possibility of replacing individual parts (modules) with new ones, which allow not only to resist aging, but also to improve the quality of the system compared to the original state. Such improvement of an artificial system is usually called development. It also includes improving the characteristics of modules, connecting new modules, accumulating information for its better use, and sometimes restructuring the hierarchy of connections.
The main uncertainties in a stochastic system are considered to be investigated at stage 5. However, indeterminacy is always present in a system that is not designed to work in conditions of a random nature of inputs and connections. Let us add that the consideration of uncertainties in this case usually turns into a study of the sensitivity of the most important properties (outputs) of the system. Sensitivity is understood as the degree of influence of a change in inputs on a change in outputs.
Stage 9. Study of functions and processes in the system in order to manage them. Introduction of management and decision-making procedures. Control actions as control systems. For purposeful and other systems with control, this stage has great importance. The main controlling factors were understood in Stage 3, but there it was general information about the system. In order to effectively introduce controls or study their effects on system functions and processes, deep knowledge of the system is required. That is why we are talking about the analysis of controls only now, after a comprehensive consideration of the system. Recall that management can be extremely diverse in content - from commands of a specialized control computer to ministerial orders.
However, the possibility of a uniform consideration of all targeted interventions in the behavior of the system makes it possible to speak not about individual management acts, but about a management system that is closely intertwined with the main system, but clearly stands out in terms of functionality.
At this stage, it is clarified where, when and how (at what points in the system, at what moments, in what processes, jumps, selections from the population, logical transitions, etc.) the control system affects the main system, how effective it is, acceptable and conveniently implemented. When introducing controls in the system, options for translating inputs and constant parameters into controlled ones should be investigated, acceptable control limits and methods for their implementation should be determined.
After the completion of stages 6-9, the study of systems continues at a qualitatively new level - a specific stage of modeling follows. We can talk about creating a model only after a complete study of the system.
target
Main Function 2
Main Function 1
Flash function 2
Flash feature 1
Flash function 3
Flash feature 1
Flash function 2
System methods and procedures. What types of mathematical models according to the construction method do you ...
The hierarchical ordering of the world was already realized in Ancient Greece. Such orderliness is observed at any level of development of the Universe: chemical, physical, biological, social.
Hierarchy is subordination, any order of objects agreed on subordination.
The term originally arose as the name of the “service ladder” in religion, then it began to be widely used to characterize relationships in the apparatus of government, the army, etc. At present, speaking of hierarchy, they mean any order of objects agreed on subordination, the order subordination of the lowest in position and rank of persons to the highest in social organizations, when managing an enterprise, region, state, etc.
The pattern of hierarchical ordering of systems (hierarchy) means that any system consists of other systems and theoretically a higher level system can always be found, which contains systems of lower levels (L. von Bertalanffy).
Van Gig characterizes hierarchy with the following characteristics:
- - the system always consists of other systems;
- - for any particular system, a system covering it can be found;
- - of two given systems, the system that includes the other is called the higher level system;
- - the lower level system, in turn, consists of other systems, and in this respect it can be considered as a higher level system;
- - the hierarchy of systems exists due to the fact that systems are more low level are components of higher-level systems.
The regularities of hierarchy or hierarchical ordering were among the first regularities of systems theory, which L. von Bertalanffy singled out and studied.
The regularity of communicativeness means that any system is connected by many communications with the environment, which, in turn, is a complex and heterogeneous formation containing a supersystem (a higher-order system that sets the requirements and restrictions of the system under study), subsystems (lower-order systems) and systems on the same level as the one under consideration.
And so, the group of regularities includes communicativeness and hierarchy.
Communication.
Any system is not isolated from other systems, but is connected by many communications with the environment, which is a complex and heterogeneous formation containing:
- III supersystem (a system of a higher order that sets the requirements and restrictions of the system under consideration);
- Ш elements or subsystems (underlying, subordinate systems);
- Ш systems of the same level with the one under consideration.
Such a complex unity of the system with the environment is called the pattern of communication.
Due to the regularity of communication, each level of hierarchical ordering has complex relationships with the higher and lower levels. It follows that each level of the hierarchy, as it were, has the property of a "two-faced Janus":
- Ш "face", directed towards the underlying level, has the character of an autonomous whole - the system;
- Ш "face", directed towards a higher level, shows the properties of a dependent part - an element of a higher system.
Hierarchy
The pattern of hierarchy is that any system can be represented as a hierarchical formation. At the same time, the regularity of integrity operates at all levels of the hierarchy. A higher hierarchical level unites the elements of the lower one and exerts a guiding influence on them. As a result, the subordinate members of the hierarchy acquire new properties that they did not have in the isolated state. And the new whole that has arisen as a result of the union of lower elements acquires the ability to perform new functions (the pattern of emergence is manifested), which is the purpose of the formation of hierarchies. These features of hierarchical systems are observed both at the biological level of the development of the Universe, and in social organizations, in the management of an enterprise, association or state, as well as in the presentation of the concept of projects of complex technical complexes, etc.
The use of hierarchical representations turns out to be useful in the case of studying systems and problem situations with great uncertainty. In this case, there is a kind of division of the “large” uncertainty into smaller ones that are better amenable to research. Even if these minor uncertainties cannot be fully disclosed and explained, nevertheless, hierarchical ordering partially removes the general uncertainty and provides at least a more effective control solution.
Example. The specialist is tasked with estimating the demand for computers next year in city N. At first glance, the task seems very difficult - there are too many uncertainties. However, let's break the task into subtasks: to assess the need for computers in various consumer sectors (commercial organizations, government agencies, students, schoolchildren, and other individuals). With regard to each of the sectors, the task no longer seems so hopeless - even without complete information, one can estimate the need for computers. Further, each of the sectors can be divided into sub-sectors, etc.
Integrity. This term is often used as a synonym for integrity. However, they emphasize their interest not in external factors in the manifestation of integrity, but in deeper reasons for the formation of this property and, most importantly, in its preservation. Integrative are system-forming, system-preserving factors, important among which are the heterogeneity and inconsistency of its elements.
Communication
Communication. This regularity forms the basis for the definition of a system proposed by V. N. Sadovsky and E. G. Yudin in the book “Investigations in the General Theory of Systems”.
Any system is not isolated from other systems and is connected by many communications with the environment, which is a complex and heterogeneous formation containing (Fig. 4.1):
supersystem(a system of a higher order that sets the requirements and restrictions of the system under consideration);
elements or subsystems(downstream, subordinate systems);
systems of the same level as the one under consideration;
Rice. 4.1. Connections of the system with the supersystem, subsystems and systems
different levels
Hierarchy
Let's consider hierarchy as a pattern of building the whole world and any system separated from it. Hierarchical order permeates everything, from the atomic-molecular level to human society. Hierarchy as a pattern lies in the fact that the pattern of integrity is manifested at each level of the hierarchy. Due to this, new properties appear at each level, which cannot be deduced as the sum of the properties of the elements. It is important that not only the union of elements at each node leads to the appearance of new properties that they did not have, and the loss of some of the properties of the elements, but also that each member of the hierarchy acquires new properties that it does not have in an isolated state.
Thus, complex qualitative changes occur at each level of the hierarchy, which cannot always be presented and explained. But it is precisely because of this feature that the regularity under consideration leads to interesting consequences. Firstly, using hierarchical representations, you can display systems with uncertainty.
Secondly, the construction of a hierarchical structure depends on the goal: for multi-purpose situations, you can build several hierarchical structures corresponding to different conditions, and at the same time, the same components can participate in different structures. Thirdly, even with the same goal, if you entrust the formation of a hierarchical structure to different researchers, then, depending on their previous experience, qualifications and knowledge of the system, they can receive different hierarchical structures, i.e., resolve qualitative changes in different ways at each level of the hierarchy .
equifinality
This is one of the least studied patterns. It characterizes the limiting capabilities of systems of a certain class of complexity. L. von Bertalanffy, who proposed this term, defines equifinality in relation to an “open” system as the ability (in contrast to equilibrium states in closed systems) of systems completely determined by the initial conditions to achieve a time-independent state (which does not depend on its initial conditions and is determined by system parameters only). The need to introduce this concept arises starting from a certain level of complexity, for example, biological systems.
At present, a number of questions of this regularity have not been studied: what parameters in specific systems provide the equivalence property? how is this property provided? How does the pattern of equivalence manifest itself in organizational systems?
Historicity
Time is an indispensable characteristic of a system, therefore each system is historical, and this is the same pattern as integrity, integrativity, etc. It is easy to give examples of the formation, flourishing, decline and even death of biological and social systems, but for technical and organizational systems it is quite enough to determine the periods of development. hard.
The basis of the regularity of historicity is the internal contradictions between the components of the system. But how to manage the development or at least understand the approach of the corresponding period of the system's development - these questions have not yet been studied enough.
Recently, more attention has been paid to the need to take into account the laws of historicity. In particular, in systems engineering, when creating complex technical complexes, it is required at the system design stage to consider not only the issues of developing and ensuring the development of the system, but also the question of how and when to destroy it. For example, the write-off of equipment, especially complex - aviation, the "burial" of nuclear installations, etc.
