On stochastic adaptive control under quantization

This paper discusses the stochastic adaptive tracking problem with input quantization, where the unknown parameters are described as a Gauss-Markov process. Based on the analysis of the cautious control law under quantization, the innovations dual controller is proposed. The quantization errors of logarithmic quantizer introduce the excitation of parameter estimation and hence improve the total closed-loop performance. Inspired by this, we also propose an alternative approach adopting the cautious control law and the logarithmic quantization with preprocessing providing the excitation to guarantee future estimation. The proposed methods imply the exciting effect of the quantization involved in the feedback loop. Simulation illustrates our results.