Optimal controller for uncertain stochastic polynomial systems with deterministic disturbances

Abstract

This article 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. The optimal closed-form controller equations are obtained through the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, this article 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. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters and without deterministic disturbances. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.