# integrated system

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## integrated system

A system that has combined different functions together in order to work as one entity. See integration.## Integrated System

a composite entity whose parts can be regarded as systems that are linked with each other by specified relations or are joined together in a regular manner to form a single whole in accordance with certain principles. The concept of the integrated system is used in systems engineering. systems analysis, and operations research and plays an important role in the systems approach in various fields of science, technology, and the national economy. An integrated system can be broken down—not necessarily uniquely—into a finite number of parts called subsystems, and each such highest-level subsystem can in turn be broken down into a finite number of smaller subsystems. The process can be continued until we reach the first-level subsystems, which are called the elements of the integrated system. The elements either are objectively incapable of subdivision or are regarded by agreement as indivisible. Thus, the subsystem is, on the one hand, itself an integrated system consisting of several elements (lower-level subsystems) and, on the other hand, an element of a higher-level system.

At each moment in time an element of an integrated system is in one of its possible states. It changes from one state to another under the action of external and internal factors. The dynamics of the behavior of an element of an integrated system are manifested as follows: the state of the element and its output signals at each moment in time are determined by the preceding states and by the input signals that have arrived at the given moment and earlier. Here, the element’s output signals are its actions on the environment and other elements of the integrated system, and its input signals are actions from the environment and other elements of the integrated system. The environment is the aggregate of systems that are not elements of the given integrated system but whose interaction with the given system is taken into consideration in studying the given system. The elements of an integrated system do not function independently from each other but interact. The properties of an element in general depend on conditions determined by the behavior of the other elements. The properties of the integrated system as a whole are determined not only by the properties of the elements but by the nature of the interaction between the elements. If two integrated systems consist of pairwise identical elements that interact differently, the systems are considered to be two different systems.

** Typical examples.** An example of an integrated system in the field of organization of production and technology is an enterprise, viewed as an aggregate production system consisting of its constituent shops and sections. Each shop or section contains a certain number of production lines. The machines and units making up the production line are usually considered the elements of the integrated system.

Automated management science has to deal with integrated systems. An example is the process of managing an enterprise or a branch of industry. This process can be regarded as an aggregate of processes—the collection of data on the state of the controlled systems, the organizing of the information flow, the storage, transmission, and processing of information, and the synthesis of control actions.

An example of an integrated system in computer technology is the software of present-day computer systems. The software includes the operating system for controlling the sequence of computations and coordinating the work of all units of the computer system, the library of standard routines, the means of automatic programming (such as algorithmic languages, translators, and interpreting systems), service routines, and programmed check systems. Each of the above components of software can be represented as a system with a hierarchical, multilevel structure consisting of separate interrelated entities, such as programs, routines, or statements.

In the field of municipal services, an example of an integrated system is presented by the motor-vehicle traffic-control system in a large city or region of a city having congested intersections and streets with large traffic flows. In such cases, automatic traffic-control techniques are used that take into account actual traffic conditions and the capacities of the streets. Automatic city and long-distance telephone systems are also examples of integrated systems.

Many other cases of integrated systems can be found among, for example, economic, organizational, and biological systems and processes.

** Methods of investigation.** The basic method of investigation of integrated systems is mathematical modeling, which includes simulation of the processes of the integrated systems on computers (computer experiment). To model an integrated system, the series of its functions must be formalized—that is, the processes must be represented as sequences of precisely defined events, phenomena, or procedures—and then a mathematical description of the integrated system must be constructed. The elements of the integrated system are usually described in the form of dynamic systems (in the broad sense), which include, in addition to the classical dynamic systems, such other deterministic and stochastic systems as finite automatons (

*see*THEORY OF AUTOMATONS), probabilistic automatons, queuing systems (

*see*QUEUING THEORY), and piecewise-linear units.

The interaction of the elements of the integrated system is usually represented as an exchange of signals between the elements and is described by four models: (1) a model of the formation of the output signal of the element based on the conditions of the functioning of the element, (2) a model of the interrelation of elements in the integrated system through the network of communications channels that transmit the signals between the elements, (3) a model of the change in the signal as it passes through the channel, and (4) a model of the behavior of the element when it receives the signal. The first and the last models are obviously included in the model of the functioning of the dynamic system. A model of signal conversion can be obtained in a similar manner if each actual signal transmission channel (together with the selecting and converting units) is represented by the corresponding dynamic system and is viewed as an independent element of the integrated system.

When the integration of elements in the integrated system is formalized, the input or output of the element is usually represented as a set of elementary inputs or outputs on the basis of the number of characteristics that describe the corresponding signals. The characteristics of the signals are assumed to be transmitted in the integrated system independently of one another along the elementary channels connecting the inputs and outputs of the corresponding elements. The integration of the elements in the integrated system is specified by a relation that associates with the given input of the *i*th element the *j*th element’s output that is connected to the given input by an elementary channel. If the integrated system is broken down into subsystems containing two or more elements, the description of each subsystem requires a corresponding single-level chart of interconnection. In addition, a chart of second-level interconnection is needed to describe the links between subsystems. The aggregate of these interconnection charts makes up a two-level interconnection chart for the integrated system. When the subsystems are united in larger subsystems, a three-level interconnection chart is formed, and so on. Multilevel interconnection charts of a similar type are also used in integrated systems with a time-variable, controlled, or stochastic structure of links between elements. An integrated system with a multilevel interconnection chart whose elements are dynamic systems can also be considered a dynamic system. Such a system’s characteristics are determined by the characteristics of the elements and by the interconnection chart. It is therefore possible to extend to integrated systems the formulations and methods of solution of many problems associated with the analysis and synthesis of classical dynamic systems, finite and probabilistic automatons, and queuing systems.

The methods of constructing mathematical models of integrated systems and the techniques of investigating such models are the subject of a new scientific discipline that emerged in the 1960’s—the theory of integrated systems. The mathematical description of the elements of an integrated system makes use of the methods of function theory, modern algebra, and functional analysis. The investigation of the mathematical models of an integrated system usually begins with estimates of the functional characteristics, which include indexes of the efficiency, reliability, noise immunity, quality of control, and other important properties of the integrated system. From a formal point of view, these indexes are functionals defined on the set of paths of motion of the integrated system. Consideration of the dependence of the functionals on the parameters of the integrated system makes possible the use of field theory techniques in the analysis of integrated systems.

In the structural analysis of an integrated system, the relations between elements and subsystems are studied, and the role and place of each subsystem in the overall process of the system’s functioning are determined. Since the interconnection chart of any integrated-system can be represented as a set of predicates (*see*PREDICATE LOGIC) defined on the set of inputs and outputs of the system’s elements, the apparatus of mathematical logic and the theory of graphs can be used to study the structure of an integrated system. Structural-analysis techniques permit the identification of the sets of subsystems of an integrated system that are in specified relationships and allow the representation of the integrated system as a set of systems with well studied typical structures. In addition, these techniques are used to estimate the structural characteristics, which provide a quantitative representation of particular properties of the interconnection chart of the elements of the integrated system. The quantitative estimate of the functional and structural characteristics is supplemented by a qualitative investigation making use of the techniques of the qualitative theory of integrated systems. The first object of investigation here is system stability. Such investigation involves, for example, the construction of regions of stability of characteristics in the space of the inte-grated-system parameters; the identification of typical behavior of the integrated system; the estimation of the feasibility, controllability, and observability of the integrated system; and the analysis of asymptotic behavior.

The 1970’s saw the introduction of the algebraic methods of the theory of semigroups, modules, and structures into the investigation of integrated systems. Such methods are usually employed in solving problems of, for example, the dynamics of deterministic systems, the decomposition of automatons, and the theory of the realization of linear systems. Because the processes of the functioning of highly integrated systems require computer modeling, serious problems arise as the extensive requirements of the calculations increase. To reduce the amount of work required in preparing models, it is advisable to use general-purpose automated modeling algorithms that can be adapted to any specific system of a given class. The existence of a simulation model permits the use of special techniques for the identification of integrated systems and for the processing of the experimental data obtained from full-scale tests of the systems. The system being tested is regarded as an integrated system with unknown element parameters and interconnection parameters. The unknown parameters are estimated by comparing the values of the functional and structural characteristics of the integrated system as established experimentally and as a result of modeling. Corrections to the initial values of the parameters of the integrated system can then be determined, and the unknown parameters can be estimated to a sufficient accuracy by the method of successive approximations.

Analytic methods of investigating integrated systems on the basis of the theory of random processes are also being developed.

### REFERENCES

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Kovalenko, I. N. “O nekotorykh klassakh slozhnykh sistem.”

*Izv. AN SSSR: Tekhnicheskaia kibernetika*, 1964, no. 6; 1965, nos. 1 and 3.

Kalman, R., P. Falb, and M. Arbib.

*Ocherki po matematicheskoi teorii sistem.*Moscow, 1971. (Translated from English.)

Buslenko, N. P., V. V. Kalashnikov, and I. N. Kovalenko.

*Lektsii po teorii slozhnykh sistem.*Moscow, 1973.

Director, S., and R. Rohrer.

*Vvedenie v teoriiu sistem.*Moscow, 1974. (Translated from English.)

N. P. BUSLENKO