A Suboptimality Approach to Distributed H2 Optimal Control
Abstract
This paper deals with the distributed H2 optimal control problem for linear multi-agent systems. In particular, we consider a suboptimal version of the distributed H2 optimal control problem. Given a linear multi-agent system with identical agent dynamics and an associated H2 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 H2 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.
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