CHAPTER 9 - STATISTICAL MODELS, I

Abstract

This chapter illustrates the theoretical and statistical models to control theory of various systems to design models of complex systems, one has to use experimental research of the systems or their subsystems and to design the corresponding models by means of a statistical treatment of the obtained data. Models obtained by the statistical treatment of the results of experimental research of functioning systems are called statistical models. The methods for designing statistical models constitute an important branch of modern mathematical statistics. The design of a mathematical model of a real system or a process is often called an identification of this system or process. Both theoretical models deduced mathematically from primary laws as well as statistical ones obtained by statistical treatment of the results of observations may be either deterministic or stochastic. In general, the use of mathematical models consists in the determination of the values of some variables knowing the values of other variables. The values of the latter variables may be obtained as the result of observations or may be ascribed from some considerations. The invariably extending area of application of mathematical methods to control problems puts the problem to the construction of models for decision-making processes. To design more complex statistical models, in particular the models whose inputs and outputs represent functions of continuously varying arguments, it is necessary to employ the theory of random functions.