Adaptive Optimal Prescribed Performance Tracking Solutions for Multiplayer Systems With Error Constraints

This brief presents the adaptive optimal prescribed performance tracking solutions for the multiplayer nonlinear systems based on the adaptive critic learning scheme, where the tracking errors are constrained to a predefined bounded set. First, the general optimal tracking solutions of multiplayer nonlinear systems are presented. Every optimal tracking solution of multiple players consists of the steady-state part and the adaptive feedback part. The steady-state part can be obtained directly according to the tracking signal and system dynamics. Then, the adaptive feedback part can be studied with the prescribed performance constraints and adaptive critic learning such that multiple value functions achieve a Nash equilibrium with error constraints. Moreover, the convergence of the critic network weight is analyzed by the Lyapunov algorithm. Finally, simulation results and experiments are presented to demonstrate the satisfactory performance of the proposed method.