Stochastic differential system output control by the quadratic criterion. V. Case of incomplete state information

A generalization of the optimal control problem for the Ito diffusion process and a linear controlled output with a quadratic quality criterion for the case of indirect observation of the state is considered. The available solution of the problem with full information is used to synthesize control from indirect observations based on the principle of separation. The ability to separate control and state filtering tasks is justified by the properties *of the quadratic criterion used. Instead of solving the arising auxiliary problem of optimal filtering described by the general equations of nonlinear filtering based on innovation processes, it is proposed to use the estimate of the conditionally optimal filter of V. S. Pugachev. Thus, the suboptimal solution of the control problem under consideration is obtained as a result of the traditional approach to control synthesis in the problem with incomplete information, consisting in a formal replacement in solving the corresponding problem with complete information of the state variable by its estimate. Finally, a case of numerical implementation of the obtained suboptimal control is proposed. It is based on the method of computer simulation, using a common beam of simulated paths both for calculating the parameters of a conditionally optimal filter and for calculating the parameters in the original control problem.