This chapter considers the quantized linear quadratic Gaussian (QLQG) control problem, which is generalized from the classical LQG problem but with the constraint that the feedback signal is quantized by a fixed-rate quantizer. It turns out that the well-known separation principle for LQG control fails to generalize to QLQG, and this is caused by the fact that minimizing the quantization error at each time instant separately does not lead to a minimum cost globally. Here we consider the QLQG problem for a scalar system and present an adaptive quantization scheme. Using this scheme, we show that the quantization distortion order is R2^-2R for a large bit rate R. This means that the separation principle holds approximately when the bit rate is sufficient. More importantly, this adaptive quantization scheme guarantees mean-square stability for the closed-loop system.

Inspec keywords: closed loop systems; mean square error methods; feedback; linear quadratic Gaussian control

Other keywords: feedback signal; mean-square stability; quantized linear quadratic Gaussian control; scalar systems; separation principle; quantization error minimization; fixed-rate quantizer; adaptive quantization scheme; classical LQG problem; closed-loop system

Subjects: Optimal control