Application of conditional-optimal filter for synthesis of suboptimal control in the problem of optimizing the output of a nonlinear differential stochastic system

We propose a suboptimal solution for the control problem for the Ito diffusion process and linear controlled output with a quadratic quality criterion for the case of indirect observations of the state. We use the previously obtained solution of the problem with complete information, the concept of separation between control and filtering problems, and the method of conditionally optimal filtering developed by V.S. Pugachev. We propose an alternative to the traditional practical approach for the synthesis of suboptimal control in a problem with incomplete information, which consists in a formal substitution in the solution of a state with its estimate. Instead of the problem of optimizing the output generated by the original model of the differential equation, we use as the state an estimate of a conditionally optimal filter. We develop one version of the numerical implementation of the proposed algorithm based on the Monte Carlo method and computer simulation.