Structured Optimal Feedback in Multi-Agent Systems: A Static Output Feedback Perspective

TL;DR

This paper reveals that structured feedback gains naturally emerge as optimal controllers in multi-agent systems for synchronization and centroid stabilization, unifying these cases through a static output feedback framework.

Contribution

It introduces a unified static output feedback perspective for optimal control in multi-agent systems, generalizing recent results and simplifying the solution process.

Findings

Optimal feedback gains are structured as static output feedback.

The approach unifies synchronization and centroid stabilization problems.

Provides a simple, general solution for optimal control in multi-agent systems.

Abstract

In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear optimal centroid stabilization. In the former problem, the considered cost functional integrates squared synchronization error and input, and in the latter, the considered cost functional integrates squared sum of the states and input. Our approach is to view the structures in the feedback gains in terms of a static output feedback with suitable output matrices and to relate this fact with the optimal control formulations. We show that the two considered problems are special cases of a more general case in which the optimal feedback to a linear quadratic regulator problem with cost functionals integrating squared outputs and inputs is a static output feedback. A treatment in this light leads to a very simple and general solution which significantly generalizes a recent result for the linear optimal synchronization problem. We illustrate the general problem in a geometric light.