Nash Equilibrium Seeking for Multicluster Games of Multiple Nonidentical Euler–Lagrange Systems

The problem of seeking Nash equilibrium (NE) in multicluster games is studied. Different from the existing multicluster game studies, the participants considered in this article have Euler–Lagrange dynamics and cannot directly obtain the information of nonneighbor participants. Agents can only communicate through directed communication graphs. In addition, there are coupling constraints between agent decisions in the same cluster. Under the widely used assumptions, two distributed algorithms are proposed to solve the NE of the multicluster game based on gradient descent, state feedback, and consensus protocol. The convergence of the two algorithms is analyzed by singular perturbation analysis and variational analysis. The theoretical results show that the first algorithm achieves exponential convergence when the parameters are certain, while the other algorithm also achieves global asymptotic convergence when the parameters are uncertain. Finally, the effectiveness of the search strategy is verified by numerical examples.