A Suboptimality Approach to Distributed ${\mathcal{H}}_2$ Optimal Control

Abstract

This paper deals with the distributed ${\mathcal{H}}_2$ optimal control problem for linear multi-agent systems. In particular, we consider a suboptimal version of the distributed ${\mathcal{H}}_2$ optimal control problem. Given a linear multi-agent system with identical agent dynamics and an associated ${\mathcal{H}}_2$ cost functional, our aim is to design a distributed diffusive static protocol such that the protocol achieves state synchronization for the controlled network and such that the associated cost is smaller than an a priori given upper bound. We first analyze the ${\mathcal{H}}_2$ performance of linear systems and then apply the results to linear multi-agent systems. Two design methods are provided to compute such a suboptimal distributed protocol. For each method, the expression for the local control gain involves a solution of a single Riccati inequality of dimension equal to the dimension of the individual agent dynamics, and the smallest nonzero and the largest eigenvalue of the graph Laplacian.

7 pages, submitted to a conference