Control of Stochastic Systems Based on the Predictive Models of Random Sequences

Abstract

This chapter is devoted to the development of the mathematical models of stochastic control systems based on the predictive models of random sequences. In particular, the linear algorithms of the forecast of a control object state for an arbitrary number of states of an investigated object and the values of a control parameter are obtained. In a mean-square sense, the algorithms allow one to get an optimal estimation of the future values of a forecasted parameter, in case true known values for an observation interval are used, provided that the measurements are made with errors. Using an arbitrary number of non-linear stochastic relations, a predictive model of a control system is obtained as well. The schemes that reflect the peculiarities of determining the parameters of a nonlinear algorithm and its functioning regularities are introduced in the work. Developed models allows one to take the peculiarities of the sequence of the change of control object parameters into full consideration and also to make full use of all known priori and posteriori information about the random sequence that was investigated. The algorithms obtained in this chapter can be used in different areas of human activity to solve a wide range of problems of the control of the objects of stochastic nature.