Event-triggered prescribed performance control of the multiplayer game nonlinear system via integral reinforcement learning

With a view to addressing the optimal control problem of multiplayer game nonlinear systems, an event-triggered prescribed performance control method based on the fusion of integral reinforcement learning (IRL) and adaptive dynamic programming (ADP) is proposed. Firstly, an auxiliary prescribed performance function (PPF) is designed to transform the original system into an unconstrained one. Drawing on the concepts of game theory, the multi-input optimal control problem is reformulated as a mixed zero-sum (MZS) game problem. Subsequently, an IRL-based event-triggered control (ETC) method is designed with a triggering condition. In this event-triggered method, ETC is updated only when the event-triggering condition is met, which reduces unnecessary communication overhead. On the basis of IRL, a critic-only neural network (NN) is established to approximate solutions of the event-triggered Hamilton-Jacobi-Bellman (HJB) equations without using the dynamic knowledge of the system. Additionally, the Lyapunov stability theorem is employed to ensure the uniform ultimate boundedness (UUB) of the system state and neural network weights. And the Zeno behavior can be avoided. Finally, an example is provided to verify the effectiveness of the proposed method in this paper.