自适应动态规划（Adaptive Dynamic Programming, ADP）是现代控制理论中一类实现系统最优控制的方法。ADP结合了最优控制理论中的动态规划方法、机器学习方法中的强化学习思想以及神经网络方法，利用神经网络的学习和拟合能力，通过强化学习的方式正向求解最优控制，可以有效解决传统的动态规划方法中难以避免的”维数灾难“问题，在求解复杂非线性系统的最优控制问题中具有广阔的前景。面对当今工业生产和社会生活中大量出现的复杂系统，它们的非线性性、未知的（难以建模描述的）系统动态特性等特点为传统的控制理论带来了新的应用限制。此外，长时间对系统控制的求解会带来不必要的计算成本，如何高效利用资源也是当今控制领域的一个重点。本文的主要工作体现在以下两个方面。

1.研究了带有状态约束的连续时间非线性系统，设计了一个包含控制障碍函数（Control Barrier Function, CBF）的控制器，从理论上证明这个控制器的设计依然能够保证系统的稳定性。在系统的部分模型已知的情况下，运用ADP方法实现对系统的最优策略求解，并给出仿真实验验证算法的可行性。

2.研究了基于ADP方法的事件触发控制，基于Lyapunov稳定性理论，引入事件触发机制，根据系统特性设计采样时刻和时间间隙，通过对系统状态的采样获取的误差来干涉对系统状态的改变，并从理论上证明这种方法仍然能够保证系统的稳定性、神经网络拟合误差的最终一致有界性，并通过仿真实验验证算法的有效性。

Adaptive Dynamic Programming (ADP) is a method in modern control theory that enables the implementation of optimal control for systems. It combines dynamic programming methods from optimal control theory with reinforcement learning ideas from machine learning methods, along with the use of neural networks. By leveraging the learning and approximation capabilities of neural networks, ADP enables forward solving of optimal control problems through reinforcement learning. It effectively addresses the "curse of dimensionality" issue that is often encountered in traditional dynamic programming approaches. ADP has promising prospects in solving optimal control problems for complex nonlinear systems. In the face of the increasing complexity of systems in industrial production and social life, characterized by nonlinearity and unknown (difficult to model) system dynamics, traditional control theory is facing new application limitations. Additionally, solving control problems for extended periods of time can result in unnecessary computational costs. Therefore, efficient resource utilization has become a major focus in the field of control. This article's main contributions are reflected in the following two aspects.

1.A controller is designed for continuous-time nonlinear systems with state constraints, incorporating a Control Barrier Function (CBF). The theoretical analysis proves that this controller design guarantees system stability. In cases where partial models of the system are known, the ADP method is employed to achieve optimal strategy solutions for the system. Simulation experiments are conducted to validate the feasibility of the algorithm.

2. Research on event-triggered control based on the ADP method has been conducted. Grounded in Lyapunov stability theory, this approach introduces an event-triggering mechanism. Sampling instants and time intervals are tailored to system characteristics. System state changes are intervened by sampling errors, ensuring system stability. Theoretical proof establishes that this method guarantees system stability and maintains the ultimate boundedness of neural network approximation errors. Simulation experiments validate the effectiveness of the algorithm.