A graph-informed regret metric for optimal distributed control

TL;DR

This paper introduces a graph-informed regret metric for designing distributed controllers in large-scale systems, enabling better disturbance mitigation by emulating an oracle with augmented information.

Contribution

It proposes the spatial regret metric, a convex reformulation, and a scalable distributed optimization method for improved distributed control based on graph structure.

Findings

Controllers optimized with spatial regret outperform classical metrics in localized disturbance mitigation.

The proposed method scales to large networks through a distributed optimization approach.

Numerical experiments on power systems validate the effectiveness of the new controllers.

Abstract

We consider the optimal control of large-scale systems using distributed controllers with a network topology that mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric that measures the worst-case performance gap between a distributed controller and an oracle which is assumed to have access to additional sensor information. The oracle's graph is a user-specified augmentation of the available information graph, resulting in a benchmark policy that highlights disturbances for which additional sensor information would significantly improve performance. Minimizing spatial regret yields distributed controllers-respecting the nominal information graph-that emulate the oracle's response to disturbances that are characteristic of large-scale networks, such as localized perturbations. We show that minimizing spatial regret admits a convex reformulation as an infinite program with a finite-dimensional approximation. To scale to large networks, we derive a computable upper bound on the spatial regret metric whose minimization problem can be solved in a distributed way. Numerical experiments on power-system models demonstrate that the resulting controllers mitigate localized disturbances more effectively than controllers optimized using classical metrics.