Feedback Quantization and Bit Allocation for Networked Control Systems with Rate Limited Channels

This paper considers feedback quantization and bit allocation for networked control where observation signals are transmitted through a wireless digital communication channel. Since the channel can transmit only a limited number of bits per unit time, bits have to be allocated to each observation signal efficiently. To obtain reasonable performance at a relatively low cost, we employ feedback quantizers to quantize continuous signals. First, we express the mean squared error (MSE) of the output of a networked control system due to quantization in terms of allocated bits and feedback filters of quantizers. Then, since it is hard to obtain the optimal bit allocation and feedback filters that jointly minimize MSE, we propose a heuristic design that iteratively optimizes bit allocation and feedback filters. The bits are allocated by a greedy algorithm, whereas feedback filters are designed by solving optimization problems. A numerical example shows that our design exhibits better performance than the conventional design.