3rd International Workshop on Linear Systems (LinSys2007)

Finite-Level Quantized Feedback Control for Linear Systems
Minyue Fu

In this talk, we study quantized feedback control of discrete-time linear systems using a finite-level quantizer. Motivated by the fact that most feedback communication channels allow a moderate bit rate, we are not particularly concerned with the problem of finding the minimum bit rate of feedback for a given control objective. Instead, we assume that a moderate bit rate is available and our task is to find a practical quantization strategy that achieves a given control objective. We introduce a simple dynamic scaling method and combine it with a known logarithmic quantization method. Using this approach, satisfactory control of linear systems can be achieved using a quantizer with a moderate number of quantization levels. Two main advantages of this approach are

  1. It is very easy to implement, and
  2. The closed-loop system behaves as if there were no limitation on the number of quantization levels when the state of the system is within a "normal" operating range.

These features are important for practical applications of quantized feedback control.