Optimal controller for uncertain stochastic polynomial systems with deterministic disturbances

This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with unknown coefficients and matched deterministic disturbances over linear observations and a quadratic criterion. As intermediate results, the paper gives closed-form solutions of the optimal regulator, controller, and identifier problems for stochastic polynomial systems with linear control input and a quadratic criterion. The original problem for uncertain stochastic polynomial systems with matched deterministic disturbances is solved using the integral sliding mode algorithm.