Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems

TL;DR

This paper demonstrates that in networked linear-quadratic control systems, increasing the decentralization parameter $ abla$ allows distributed controllers to nearly match centralized optimal performance, with performance gap shrinking exponentially.

Contribution

It introduces a $ abla$-distributed control framework that quantifies the trade-off between decentralization and performance, showing near-optimal results with moderate decentralization levels.

Findings

Performance difference diminishes exponentially with increasing $ abla$.

Distributed control achieves near-centralized optimality under mild assumptions.

The approach is effective for large-scale 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 $\kappa$-distributed control, which lets the agents make control decisions based on the state information within distance $\kappa$ on the underlying graph. This controller can tune its degree of decentralization using the parameter $\kappa$ 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 $\kappa$-distributed control and centralized optimal control becomes exponentially small in $\kappa$. 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.