Identification and Control of Multidimensional Delayed Processes in Conditions of Incomplete Information

Abstract

Problems of identification and control of multidimensional discrete-continuous processes with delay in conditions of incomplete information about the object are considered. In such conditions, the form of parametric equations for various channels of the object is absent due to the lack of a priori information. Moreover, multidimensional processes have stochastic dependences of the components of the vector of output variables. Under such conditions, the mathematical description of such processes leads to a system of implicit equations. Nonparametric identification and control algorithms for multidimensional systems are proposed. The main task of modeling such processes is to determine the predicted values of the output variables from the known input. Moreover, for implicit equations, it is only known that one or another output variable can depend on other input and output variables that determine the state of a multidimensional system. In this study, a nontrivial situation arises when solving a system of implicit equations under conditions when the dependences between the components of the output variables are unknown. The application of the parametric theory of identification in this case will not lead to success. One of the possible directions is the use of the theory of nonparametric systems. The main content of the work is the solution of the identification problem in the presence of dependencies of the output variables and then the solution of the control problem for such a process. Here you should pay attention to the fact that when determining the reference actions for a multidimensional system, it is first necessary to solve the system of reference actions, since it is not possible to choose arbitrarily setting influences from the range of definition of output variables. Computational eXperiments aimed at investigating the effectiveness of the proposed identification and control algorithms are presented.