Optimal Finite-Dimensional Controller of a Stochastic Differential Object’s State by Its Output. II. Stochastic Measurements and Separation Theorem

Consideration is continued of the problem of the inertial control law by the output synthesis of a continuous nonlinear stochastic object, which is optimal on average and on a finite time interval, and works with the desired speed. An algorithm for synthesizing the optimal structure of a dynamic controller of a selected finite order, obtained in the first part of the article for the case of accurate measurements of the control object’s state variables part, is presented. Its application is demonstrated in detail for the case when the state variables of the control object are measured with random errors. Using the example of a linear-quadratic-Gaussian problem, it is shown that the proposed controller of the corresponding order also satisfies the well-known separation theorem.