Decentralized multi-controller stabilizability over communication channels

Abstract

We study the problem of distributed control over communication channels, where a number of distributed stations stabilize a linear system. We quantify the rate requirements and obtain optimal signaling, coding and control schemes for decentralized stabilizability in such multi-controller systems. We show that in the absence of a centralized decoder at the plant, there is in general a rate-loss in decentralized systems as compared to a centralized system. This result is in contrast with the lack of rate loss in the stabilization of multisensor systems. Furthermore, there is also a rate loss if explicit channels are available between the stations. We obtain the minimum data rates needed in terms of the open-loop system matrix and the connectivity graph of the decentralized system, and obtain the optimal signaling policies. We also present constructions leading to stability. In addition, we show that if there are dedicated channels connecting the controllers, rate requirements become more lenient, and as a result strong connectivity is not required for decentralized stabilizability. We determine the minimum number of such external channels leading to a stable system, in case strong connectivity is absent.