Two-Timescale Distributed Approach to Nash Equilibrium Seeking of Euler–Lagrange Systems in Multicluster Nonconvex Games
Banghua Huang, Yang Liu, Jianquan Lu, Yunliang Jiang, Weihua Gui · IEEE Transactions on Automatic Control · 2025
In this paper, we investigate a distributed generalized Nash equilibrium (GNE) seeking problem for multi-cluster games, where each cluster consists of multiple players. Different from most of the existing multi-cluster game studies, the multi-cluster games considered nonconvex cost functions, nonconvex (coupled) inequality constraints, and nonaffine (coupled) equality constraints. Each player in a cluster communicates and cooperates with other players based on a directed connected network to make optimal actions that minimize the cost function of their cluster. We propose a two-timescale multi-agent system (MAS) for multi-cluster nonconvex games. We further propose a two-timescale MAS in which players are formulated by Euler-Lagrange (EL) dynamics. We prove the convergence of the MAS with derived conditions to one of the local GNEs. We elaborate on a numerical example, a price-bidding problem in an electricity market, and a Nash-Cournot game to illustrate the characteristics of the proposed approach.