Structure Preserving H-infinity Optimal PI Control

TL;DR

This paper proves that a multi-variable PI controller is optimal for a class of networked control systems with performance measured by frequency weighted H-infinity norms, ensuring decentralized control based on local node states.

Contribution

It introduces a novel optimal control design for networked systems, demonstrating the effectiveness of structure-preserving PI controllers in complex multi-variable settings.

Findings

Optimal PI controller is decentralized for networked systems.

Controller achieves frequency weighted H-infinity norm performance.

Control action depends only on local node states.

Abstract

A multi-variable PI (proportional integrating) controller is proved to be optimal for an important class of control problems where performance is specified in terms of frequency weighted H-infinity norms. The problem class includes networked systems with a subsystem in each node and control action along each edge. For such systems, the optimal PI controller is decentralized in the sense that control action along a given network edge is entirely determined by states at nodes connected by that edge.