Distributed Nash Equilibrium Seeking for Constrained Multicluster Games of Second-Order Nonlinear Multiagent Systems

This article investigates multicluster games (MCGs) of multiagent systems, where the players are subject to nonlinear inequality constraints. In contrast to existing MCGs, our problem involves the second-order nonlinear dynamics of players. Due to the second-order nonlinear dynamics, existing Nash equilibrium (NE) seeking algorithms cannot deal with our problem. Also, the second-order nonlinear dynamics and the nonlinear inequality constraints make it difficult to design and analyze distributed algorithms for our problem, because it is hard for the players to satisfy the inequality constraints as a result of the second-order dynamics and the inequality constraints must be satisfied by the NE of the MCGs. In order to control these heterogeneous second-order nonlinear players to autonomously seek the NE of the MCGs, we design a distributed algorithm via gradient descent and state feedback. With the help of Lyapunov stability theory, we analyze the convergence of the algorithm. Under the algorithm, the second-order players globally converge to the NE. Finally, the simulation example of electricity market games verifies the effectiveness of the algorithm.