The complex braid of communication and control
Abstract:
Fundamental problems in communication and control are strongly tied in modern cyberphysical systems. In this paper, we review the problem of mean-square stabilization of a discrete-time linear dynamical system where the estimated state is transmitted for control over a digital communication channel. This arises in several emerging applications including remote robot control, automated highway navigation using wireless sensor systems, and automatic control for pursuit evasion games. In this context, a data-rate theorem refers to the minimum information rate required to guarantee the stability of the system over a given communication channel. Loosely speaking, it states that the information rate to be supported by the channel must be large enough compared to the unstable modes of the system, so that it can compensate for the expansion of the state during the communication process.
Since its first rigorous formulation about a decade ago, and driven by technological advancements of embedded systems for control, there has been a growing interest in stating a data rate theorem for the most general communication model. We review a series of contributions by different groups (including ours), sketching mathematical arguments based on a blend of information-theoretic and control-theoretic tools. We will also try to draw a connection between results in control and some recent advancements in feedback communication and will conclude mentioning some open problems in the field.