Information-constrained Optimal Control of Distributed Systems with Power Constraints

TL;DR

This paper develops a method for optimal control of interconnected systems with communication delays and power constraints, reformulating the problem to enable offline computation of control gains.

Contribution

It introduces a novel approach to solve information-constrained optimal control problems with power constraints by reformulating as a linear covariance problem and exploiting duality.

Findings

The method effectively handles communication delays and power constraints.

Optimal control gains can be computed offline.

The approach ensures minimal finite-horizon quadratic cost.

Abstract

In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by optimally choosing the control inputs for the subsystems, accounting for power constraints in the overall system and different information available at the decision makers. To this purpose, due to the quadratic nature of the power constraints, the LQG problem is reformulated as a linear problem in the covariance of state-input aggregated vector. The zero-duality gap allows us to equivalently consider the dual problem, and decompose it into several sub-problems according to the information structure present in the system. Finally, the optimal control inputs are found in a form that allows for offline computation of the control gains.