Problem of Modeling and Control of Multi-Dimensional Timeless Processes with Dependent Output Variables

Abstract

In this paper, we consider the problems of modeling and controlling multidimensional inertialess systems with delay under nonparametric uncertainty. We are talking about the multidimensional processes which are in conditions where the form of parametric equations for various channels of the object is absent due to lack of a priori information. The main emphasis is placed on the case when the components of the vector of output variables are randomly connected in an unforeseen way. In the case of a stochastic dependence of the output variables, the mathematical description of the object is reduced to a system of implicit equations, the form of which is unknown. Therefore, the main task of modeling is to find the predicted values of output variables from known input variables. When managing a multidimensional object, an important feature is the definition of setting actions. The main thing here is that the setting influences of the control system should not be chosen arbitrarily from the corresponding areas, but depending on the definition of the previous ones. Nonparametric identification and control algorithms for multidimensional systems are proposed. Computational experiments that show the efficiency of using the proposed nonparametric identification and control algorithms are presented.