In this article, an integral reinforcement learning-based dynamic event-triggered safety control scheme is proposed to tackle the multiplayer Stackelberg–Nash games (MSNG) problem in continuous-time nonlinear systems with time-varying state constraints. Initially, a new barrier function (BF) is introduced by integrating traditional barrier functions with a novel smooth function to address the challenge of time-varying state constraints. Then, the constrained MSNG system is transformed into an unconstrained system through the application of the state transformation technique, which helps to characterize hierarchical decision problems as MSNG problems with the leader and followers. Meanwhile, the integral reinforcement learning (IRL) technique is also applied to ease the demand for precise system dynamics. Moreover, a new dynamic event-triggered control (DETC) mechanism is designed, resulting in coupled dynamic event-triggered Hamilton–Jacobi (HJ) equations. A single critic neural network (NN) is constructed to learn the optimal control laws for the leader and followers. By employing Lyapunov theory, the integral reinforcement learning-based dynamic event-triggered safety control method ensures that the system state and the critic NN weight errors are uniformly ultimately bounded (UUB). Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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具有时变状态约束的多人Stackelberg-Nash博弈的基于积分强化学习的动态事件触发安全控制

在本文中，提出了一种基于积分强化学习的动态事件触发安全控制方案，以解决具有时变状态约束的连续时间非线性系统中的多人Stackelberg-Nash博弈（MSNG）问题。最初，通过将传统障碍函数与新颖的平滑函数相结合，引入了新的障碍函数（BF），以解决时变状态约束的挑战。然后，通过状态转换技术的应用，将受约束的MSNG系统转变为无约束的系统，这有助于将层次决策问题表征为具有领导者和跟随者的MSNG问题。同时，还应用积分强化学习（IRL）技术来缓解对精确系统动力学的需求。此外，设计了一种新的动态事件触发控制（DETC）机制，产生耦合动态事件触发的汉密尔顿-雅可比（HJ）方程。构建单个批评神经网络（NN）来学习领导者和追随者的最优控制律。基于积分强化学习的动态事件触发安全控制方法利用李亚普诺夫理论，保证系统状态和临界神经网络权重误差一致最终有界（UUB）。最后，提供了两个仿真例子来证明所提算法的有效性。