To communicate or not to communicate: A decision-theoretic approach to decentralized adaptive control

It was recently shown that adaptive laws, for the adjustment of control parameters in strictly decentralized control systems with unknown parameters, can be developed to assure stability, provided prior information is available concerning the objectives of the various subsystems. However, while this can be theoretically justified, practical simulation studies have shown that the transient responses of the subsystems will be generally prohibitively large. To overcome this problem, the authors have been studying the possibility of using limited communication between subsystems to improve the responses significantly. This paper discusses in detail the stability and performance questions in such systems, and demonstrates that substantial improvement in performance may be possible with very little communication at critical instants. First, the paper discusses the communication problem as a switching problem, in which the controllers switch between two different adaptive laws, when there is no communication and over intervals when communication takes place. It is shown using a common quadratic Lyapunov function, that the stability and performance issues can be decoupled. Next, by attaching a cost for communication between subsystems as well as the errors at the outputs, the problem is cast as an optimization problem. Extensive simulation studies on a network containing six subsystems are included to indicate the effect of intermittent communication on performance.