Optimal Controller for Stochastic Polynomial Systems with State-Dependent Polynomial Input

Abstract

This paper presents an optimal quadratic-Gaussian controller for stochastic polynomial systems with a state-dependent polynomial control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for polynomial systems with a state-dependent polynomial control input and a quadratic criterion. Performance of the obtained optimal controller is verified in an illustrative example against a conventional linear-quadratic-Gaussian (LQG) controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.