An Unknown Multiplayer Nonzero-Sum Game: Prescribed-Time Dynamic Event-Triggered Control via Adaptive Dynamic Programming

In this paper, the novel prescribed-time dynamic event-triggered control method of an unknown multiplayer nonzero-sum game (MP-NZSG) is designed by using adaptive dynamic programming (ADP). Firstly, a neural network-based identifier is constructed to estimate the unknown system dynamics. Subsequently, a novel ADP-based dynamic event-triggered control approach is advanced to ensure optimality and prescribed-time stability. A critic neural network (NN) is established for each player to approximate the Nash equilibrium solution of the dynamic event-triggered Hamilton-Jacobi-Isaacs (HJI) equation. This network employs a novel weight updating law, based on the experience replay technique, to alleviate the persistence of excitation condition. Furthermore, using the Lyapunov method, the uniform limit boundedness analysis of the neural network approximation error and multiplayer system is validated. Additionally, minimum inter-event time (MIET) is conclusively established to mitigate the notorious Zeno behaviour. Ultimately, the efficacy of the proposed method is rigorously substantiated through comprehensive simulation results. Note to Practitioners - Our research addresses the challenges of multi-component coordinated control, particularly in spacecraft attitude control. To handle these complexities, we propose an innovative adaptive dynamic event-triggered control approach. By integrating adaptive dynamic programming and neural networks, we effectively model and manage unknown system dynamics, enhancing the controller's adaptability and robustness. Dynamic event-triggered policies are introduced to optimize system performance and reduce computational costs. The ADP-based prescribed time optimal control scheme prioritizes steady-state performance of nonlinear nonaffine systems, ensuring precise task completion within specified timeframes. Additionally, experience replay technology further fortifies the controller's learning and adaptability to dynamic environments.