Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems

Abstract

This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called -distributed control, which lets the agents make control decisions based on the state information within distance on the underlying graph. This controller can tune its degree of decentralization using the parameter and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a subexponentially growing graph condition, the performance difference between -distributed control and centralized optimal control becomes exponentially small in . This result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.