Discrete time LQG controls with control dependent noise

Abstract

This paper presents some studies on partially observed linear quadratic Gaussian (LQG) models where the stochastic disturbances depend on both the states and the controls, and the measurements are bilinear in the noise and the states/controls. While the Separation Theorem of standard LQG design does not apply, suboptimal linear state estimate feedback controllers are derived based on certain linearizations. The controllers are useful for nonlinear stochastic systems where the linearized models include terms bilinear in the noise and states/controls and are significantly more accurate than if the bilinear terms are set to zero. The controllers are calculated by solving a generalized discrete time Riccati equation, which in turn has properties relating to well posedness of the associated LQG problem.