A Suboptimality Approach to Distributed H Optimal Control
Junjie Jiao, Harry L. Trentelman, M. Kanat Camlibel · IFAC-PapersOnLine · 2018
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, an associated H2 cost functional, and a desired upper bound for the cost, our aim is to design a distributed diffusive static protocol such that the protocol achieves state synchronization while the associated cost is smaller than the given upper bound. To that end, we first analyze the H2 performance of linear systems and then apply the results to linear multi-agent systems. Based on these results, 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 Laplacian matrix.