Nash Equilibrium Seeking for Multi-Cluster Games of Second-Order Systems Over Weight-Unbalanced Digraphs

In this brief, the multi-cluster game of second-order systems over weight-unbalanced directed graphs is studied for the first time, where each local cost function depends on the decisions of all participants. A novel algorithm is designed based on state feedback and left eigenvector estimation under the partial information setting, where each agent only knows its own local decision and cost function information. It is demonstrated by Lyapunov stability theory that the algorithm can converge to the Nash equilibrium (NE) with the weight-unbalanced directed graphs. Finally, the effectiveness of the algorithm is illustrated by a numerical simulation.