Adaptive Prescribed-Time Distributed Nash Equilibrium Seeking for Networked Games With Heterogeneous Dynamics and Unknown Uncertainties

This paper investigates the adaptive prescribed-time distributed Nash equilibrium (NE) seeking problems for networked games with heterogeneous dynamics and unknown uncertainties. The proposed algorithms are based on the two-layer structure, namely the NE seeking part and the tracking control part. For the players without uncertainties, the adaptive parameters are utilized in the seeking part to avoid the use of the global information. The auxiliary variables are constructed to seek for the NE point within the prescribed time and serve as the reference signals for the tracking control part. Then the state feedback control is designed to drive the strategies of all the players to the expected NE point in the prescribed time. Furthermore, the approximation theory is introduced to deal with the unknown nonlinear uncertainties. The exponential parameters are involved in the designed estimates to accelerate the convergence rate. The Lyapunov method is utilized to show the prescribed-time convergence property of the algorithms. Besides, although the time-varying piecewise function is involved in the algorithms, the uniform boundedness of the control input can be ensured by carefully selecting the initial values of the auxiliary parameters. Finally, the simulation is given to show the effectiveness of the proposed algorithms.