Linear quadratic Gaussian control with quantised innovations Kalman filter over a symmetric channel

Abstract

This study discusses the quantised linear quadratic Gaussian (LQG) control problem for linear stochastic systems. A symmetric channel that connects the sensor and the controller is considered. Given a quantiser that is applied on the most recent innovation of the measurement, it is shown that the well-known separation principle remains valid. Based on a quantised innovations Kalman filter, a suboptimal LQG controller is given in terms of the solutions of two Riccati difference equations associated, respectively, with the state estimation and the standard linear quadratic regulator control. The corresponding approximate suboptimal cost is also derived. An illustrative example is included to demonstrate the effectiveness of the proposed controller.