Research On Distributed Nash Equilibrium Search Algorithm For Multi-agent Cluster Game

Multi-agent distributed cluster game aims to explore the cooperation and competition behavior of groups by the relevant concepts and ideas of game theory and the theories of distributed optimization and decision control.In this paper,we consider the unconstrained and constrained distributed cluster game(generalized)Nash equilibrium problem under directed graph.The main work is summarized as follows:(1)The Nash equilibrium search problem of multi-agent cluster game with lost communication and without lost communication under strong connected switching topology is studied,and the distributed algorithms are proposed respectively.Firstly,for the problem of decision estimation,the cluster communication topology is reconstructed with the idea of hierarchical network,and the distributed decision and cost function estimators are designed.Then,based on the gradient method,the corresponding distributed Nash equilibrium seeking strategy is designed.Finally,the stability of the algorithm is proved by Lyapunov stability theory and singular perturbation analysis method.(2)The Nash equilibrium search problem of multi-agent cluster games under the joint strongly connected switching topology is studied,and the distributed solution strategy under the dual time scale is proposed.Firstly,by analyzing the influence of topology graph on algorithm design,a cluster cost function estimation method is proposed in the joint strongly connected switching topology,and a(semi)distributed Nash equilibrium search algorithm is designed respectively for the case that agent knows the global and partial decision information.Finally,under different assumptions,the local and non-local convergence results of the algorithm are given respectively.(3)The generalized Nash equilibrium search problem of multi-agent cluster game for heterogeneous nonlinear Euler-Lagrange systems is studied,and the parameter dependent and parameter independent distributed algorithms are designed respectively.Firstly,by the variational analysis method,it is proved that the solution of the variational inequality is the variational generalized Nash equilibrium of the problem under certain conditions.Then,based on the state feedback and tracking control methods,the corresponding distributed generalized Nash equilibrium solution strategy is designed.Finally,it is proved that the algorithm is globally exponentially convergent when the parameters are available and globally asymptotically convergent when the parameters are uncertain.(4)The generalized Nash equilibrium search problem of cluster games with mixed heterogeneous dynamics is studied,and a predefined-time generalized Nash equilibrium seeking algorithm is proposed.By constructing exact penalty function and the time base generator,the problems of inequality constraints and discontinuous control behavior in the cluster are solved respectively,and the parameters dependent and independent distributed generalized Nash equilibrium search algorithm is designed.It is proved that the algorithm can converge at the specified time by the user without relying on the initial value.Finally,the effectiveness of the algorithm is verified by simulation.