Accelerated Nash Equilibrium Seeking for Constrained Multi-Cluster Games With Time-Varying Communication
Rui Zhu, Fuyong Wang, Zhongxin Liu, Zengqiang Chen · IEEE Transactions on Circuits and Systems I Regular Papers · 2025
This paper proposes a distributed accelerated Nash equilibrium (NE) seeking algorithm for constrained multi-cluster games with time-varying communication, where agents in the same cluster are cooperative, while there is competition among different clusters. Constraint sets and time-varying interaction networks are considered simultaneously, which is motivated by their widespread presence in practical applications, thereby the designed algorithm can deal with more scenarios where cooperation and competition coexist. To attain higher flexibility and faster convergence, two acceleration techniques, named the heavy-ball method and Nesterov momentum, are introduced into the algorithm with distinct parameters, and an average parameter is employed to handle constraints. Furthermore, the linear convergence of the algorithm to NE is confirmed based on the optimality gap, the state difference, the consensus error and the gradient tracking error, and explicit bounds for the step size and parameters are derived by the associated properties of the time-varying networks and cost function. Finally, the acceleration effect of the algorithm is demonstrated in the energy management system, which validates the feasibility of the designed algorithm.