Research On Nash Equilibrium Seeking Problem Of Noncooperative Games In Hybrid Multi-Agent Systems

Noncooperative games of multi-agent systems have become one of the hot topics in the research of control theory.Due to agents involved in different game tasks are different from others,and the physical dynamics of agents often show different characteristics.Therefore,this paper mainly focuses on the hybrid multi-agent systems composed of second-order linear dynamic and Euler-Lagrange dynamic,and studies two kinds of noncooperative game with predefined time convergence and unknown information in directed communication graphs,the research contents are as follows:For the hybrid multi-agent systems with global equality constraints,the distributed generalized Nash equilibrium seeking of noncooperative game with predefined time convergence is proposed.The consensus protocol is used to estimate the decision information of non-neighbors,by introducing the time-based generator,and based on the gradient descent method and the state feedback method,a distributed Nash equilibrium search algorithm is designed to control the agents involved in the game to seeking the generalized Nash equilibrium at the predefined time.By singular perturbation and Lyapunov stability analysis,it is proved that the proposed algorithm can converge to generalized Nash equilibrium in a predefined time.The effectiveness of the algorithm is verified by a numerical simulation example.For the hybrid multi-agent systems of the noncooperative games with convex set constraints,the parameters of the dynamic systems and cost function form are unknown,an extremum seeking-based approach for generalized Nash equilibrium seeking is proposed.The auxiliary system is introduced,based on projection operation and distributed consensus protocol,the cost function gradient of the agent is estimated by using the adaptive extremum search strategy.The PI controller is designed based on the backstepping method for trajectory tracking to achieve the generalized Nash equilibrium solution of the problem.The theoretical results show that the designed algorithm converges to the neighborhood of the generalized Nash equilibrium.The effectiveness of the algorithm is verified by an example of mobile sensor connectivity control.