H∞ Controller Design for a Multi-Agent System Based on a Replicated Control Structure

Several recent design techniques address the problem of distributed controller synthesis for multi-agent systems (MAS). However, since these methods use a decomposition based approach to reduce the complexity of the MAS, they cannot provide a guarantee of performance with the designed controller, and furthermore lead to conservative designs due to the Lyapunov shaping paradigm. This paper proposes a direct gradient-based-optimization synthesis technique for a MAS with fixed communication topology, exploiting the fact that the same controller is replicated on each agent. Although this results in a non-convex design problem, an appropriate initialization step makes the synthesis efficient and helps to obtain controllers with guaranteed performance on the MAS.