LQG control with quantized innovation Kalman filter

The purpose of this paper is to extend our previous work on the multi-level quantized innovation Kalman filter(MLQ-KF). We consider the linear quadratic Gaussian (LQG) optimal control problem in the discrete systems. Under the assumption that the innovation is approximately Gaussian, it is shown that the separation principle remains valid under the quantized measurement output. The optimal LQG controller is then given in terms of two Riccati difference equations associated respectively with the quantized Kalman filter and the standard LQR control. The corresponding minimum cost is also derived. An illustrative example is included to benchmark our proposed quantized LQG control with the standard LQG control.