Optimal synchronization of circulant networked multi-agent systems

This paper investigates the synchronization problem of identical agents while minimizing an LQ-based performance index that reflects the behavior of the synchronization errors. For an objective function which penalizes the synchronization errors with a circulant structured weighting matrix, an optimal networked controller is proposed which has the same structure. The resulting communication graph is a linear combination of circulant subgraphs which couple all agents with all other agents.