Distributed generalized Nash equilibrium seeking strategy design for multi‐cluster games of high‐order players

Abstract

In this paper, a multi‐cluster game (MCG) of autonomous players is explored. Different from the existing MCGs, the high‐order dynamics of players is taken into account in our problem. Owing to the high‐order dynamics of players, existing strategies for MCGs are unable to tackle our problem. For purpose of seeking the variational generalized Nash equilibrium (vGNE) of the game, a distributed strategy is designed on the basis of gradient descent and state feedback, in which a distributed estimator is embedded for the players to estimate the decisions of other players. Furthermore, the asymptotical convergence of the strategy is analyzed via Lyapunov stability theory and variational analysis. Finally, the effectiveness of our method is verified through a numerical simulation.