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

This article 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 players without uncertainties, adaptive parameters are utilized in the seeking part to avoid the use of global information. Auxiliary variables are constructed to seek the NE point within the prescribed time and serve as reference signals for the tracking control part. Then, 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 unknown nonlinear uncertainties. 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, a simulation is given to show the effectiveness of the proposed algorithms.