Control Communication Complexity of Nonlinear Systems

Abstract

The interaction of information and control has been a topic of interest to system theorists that can be traced back at least to the 1950’s when the fields of communications, control, and information theory were new but developing rapidly. Recent advances in our understanding of this interplay have emerged from work on the dynamical effect of state quantization together with results connecting communication channel data rates and system stability. Although this work has generated considerable interest, it has been centrally concerned with the relationship between control system performance and feedback information processing rates while ignoring the complexity (i.e. the cost of information processing). The concepts of communication and computation complexity of a controlled dynamical system based on digitized information lie in what is largely an uncharted area. In our recent work an attempt was made to explore this area by introducing a new measure of communication complexity for a two-player distributed control system. This complexity is named control communication complexity (CCC). It is based on the communication complexity concept defined in distributed computing and seeks to connect the complexity of information exchange over finite bandwidth channels with the control system dynamics. The purpose of the present paper is to extend the study of control communication complexity to an interesting class of continuous-time control systems that have appeared in the recent literature dealing with quantum communication and control systems. An interesting aspect of this extension is that it brings together heretofore independent research themes that have been prominent in the research career of Roger Brockett.