Generalized Nash equilibrium seeking algorithm design for distributed constrained noncooperative games with second-order players

In this paper, we study the noncooperative games of multi-agent systems. Different from the well-known noncooperative games, our problem involves not only the coupling inequality constraints and the local inequality constraints of decisions, but also the second-order dynamics of players. Due to the second-order dynamics and the inequality constraints, existing generalized Nash equilibrium seeking algorithms for noncooperative games cannot solve our problem. Besides, the second-order dynamics together with the inequality constraints give rise to the difficulties in distributed algorithm design and analysis. In order to seek the variational generalized Nash equilibrium of the games, we design a distributed algorithm based on gradient descent, state feedback and projection operations. Moreover, we analyze the asymptotic convergence of the algorithm via variational analysis and Lyapunov stability theory. Finally, two examples verify the effectiveness of the algorithm. (c) 2022 Elsevier Ltd. All rights reserved.