Feedback Control via Integrated Sensing and Communication: Uncertainty Optimisation

Abstract

This paper studies integrated sensing and communication (ISAC) coordination for feedback control tasks under shared platform constraints. We consider a cyber-physical system in which a remote dynamical process (i.e., remote source) is regulated with the support of an ISAC-enabled base station that alternates between sensing the source state and communicating control-relevant information to the source, with the two operations semantically intertwined rather than serving separate targets and users. For a Gauss-Markov source with Bernoulli-distributed sensing and communication links and a finite-horizon linear-quadratic-Gaussian (LQG) cost, we derive the optimal ISAC and control policies. Under a Bellman-operator condition, we prove that the optimal ISAC policy at the base station follows an order-threshold structure in terms of the source and base-station estimation covariances, while the optimal control policy at the source follows a certainty-equivalent structure in terms of the source state estimate. We show that the threshold region, defined as the set of estimation covariance pairs for which communication is preferred over sensing, expands with increasing source uncertainty and contracts with increasing base-station uncertainty. Our numerical analysis validates the theoretical findings.