Integrated Control and Communication in LQG Systems

TL;DR

This paper explores how to transmit data through control signals in MIMO LQG systems without increasing control costs, providing a computable capacity expression and generalizing to Gaussian channels with feedback.

Contribution

It introduces a novel framework for integrated control and communication in LQG systems, including a computable capacity formula and analysis of data transmission at zero control cost.

Findings

Data can be transmitted at a nonzero rate without increasing control cost.

A computable capacity expression using semidefinite programming is derived.

The framework generalizes to MIMO Gaussian channels with feedback and ISI.

Abstract

In this paper, we study the Integrated Communication and Control (ICAC) problem. Specifically, we investigate how messages can be transmitted from the controller/encoder to the observer/decoder through the control signal in Multiple-Input Multiple-Output (MIMO) vector-state Linear Quadratic Gaussian (LQG) systems under control constraints. We provide a computable capacity expression using semidefinite programming. We further show that it is possible to transmit data at a nonzero rate over an LQG system while maintaining the same optimal control cost as in the case where no information message are transmitted. Finally, we discuss how this framework generalizes communication over MIMO Gaussian channels with feedback, both with and without InterSymbol Interference (ISI).