Dynamic Logarithmic Vector Quantizer Design for Stochastic Continuous Time Linear Systems With State Feedback Control

Abstract

This paper addresses logarithmic vector quantizers with dynamic sensitivity design for stochastic continuous time linear system with a feedback control law. Logarithmic vector quantization is adopted so that the coarsest density of quantization and data compression efficiency are both guaranteed. In addition, the problem of quantizer saturation is treated with the mechanism of dynamic sensitivity. The dynamic of the sensitivity during “zoom-in” / “zoom-out” stages is proposed. It is shown that with the proposed algorithm, a single input continuous time linear system can be stabilized in the sense of mean square by quantized feedback control via adopting sensitivity varying algorithm. Results from theoretical analysis are verified through simulation at the end of the paper.

Keywords

• Logarithmic quantizer
• vector quantization
• stochastic linear systems
• dynamic sensitivity
• feedback stabilization