Mean-Square Optimal Controller for Stochastic Polynomial Systems with Multiplicative Noise

This paper presents the mean-square optimal quadratic-Gaussian controller for stochastic polynomial systems with a polynomial multiplicative noise, a linear 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 stochastic polynomial systems with a polynomial multiplicative noise, a linear control input, and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQG controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.