Modeling of systems

3.1. THE TERMS " MODEL" AND " MODELLING". ABSTRACT MODEL ARBITRARY NATURE OF THE SYSTEM

As the general system theory considers not some specific systems, but general that is in various systems irrespective of their nature, a subject of its studying is abstract models of the corresponding real systems.

The model is representation of real object, system or concept in some form different from their real existence form.

Every model - is a certain analogy: for one system there has to be other system which elements from some point of view are similar to elements of the first. There has to be a display, which for elements of the modelled system puts in compliance elements of some other system - modeling. Besides, there has to be a display, which for properties of elements of the modelled system puts in compliance of elements properties of the modeling system.

In most cases, the abstract model of arbitrary nature system can be represented by scheme shown in Figure 4.1, which, in fact, is an illustration of the introduced concepts.

The system does not exist by itself, but it stands out from the surrounding environment at any systemically lines, often serves the purpose of the system. System interaction with the external environment is carried out through a system of input and output (number of input and output parameters).

Input parameters of the system are understood as a complex of parameters of the external environment (including output parameters of systems, external in relation to considered, for example, control systems) exerting considerable impact on a state and value of output parameters of the considered system and giving in to the account and the analysis means, available the researcher.

Output parameters - a set of system parameters that have a direct impact on the external environment and significant in terms of the purpose of the study.

An important functioning feature of complex systems is the fundamental uncertainty of the true state of the environment at any given time. The nature of the uncertainty associated with the presence of number of reasons, the most important is caused by the following factors.

• Perhaps, parameters of the external environment which are directly influencing behavior of system (that is parameters which should be referred to category of " entrance") the researcher often doesn't know about some, and, therefore, can't consider it.

• Some parameters of the external environment can't be measured owing to technical impracticality of information means.

• Numerical values of the considered parameters are estimated with the errors of measurements defined on the one hand - internal noise of measuring devices, and another - external hindrances.

Impact on system of similar unaccounted factors is compensated by introduction to additional communications model - the external revolting influences or " noise".

The system can be in different statuses. The status of any system at given time can be described, with a certain accuracy, set of parameter values (q) of a status.

Thus, the system is characterized by three groups of variables:

1. Input variables which are generated by systems, external rather researched;

2. Output variables defining impact of the researched system on the environment;

3. Condition parameters that characterize the dynamic behavior of the studied system.

At the research of the majority of systems all three groups of entered sizes are assumed by functions of time.