Observability and stabilisability of networked control systems with limited data rates

Abstract

ABSTRACTThis paper investigates the observability and stabilisability problem for linear time-invariant systems, where sensors and controllers are geographically separated and connected by a stationary memoryless digital communication channel. The limited information of the plant state is transmitted over such a channel to the controller. We focus on explaining the effect imposed by limited data rates. A new quantisation, coding and control scheme is presented to minimise the required data rate for observability and stabilisability. Different from prior research, our study shows that, the required data rate is determined by the state prediction error. Namely, the smaller prediction error requires the smaller codeword length, which leads to the smaller data rate. It is shown that, there exists a lower bound on the average data rate above which the system is observable and stabilisable. Illustrative examples are given to demonstrate the effectiveness of the proposed quantisation, coding and control scheme.