This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.

中文翻译：

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具有输入约束和不匹配扰动的仿射非线性系统的基于补偿器的近似最优控制

本文通过自适应动态规划 (ADP) 技术，针对存在扰动的一类约束连续时间非线性系统开发了一种新的近似最优控制方法。首先，引入辅助动态补偿器来处理输入约束。通过用设计的辅助补偿器对原系统进行增广，通过稳定等效增广系统来规避约束最优控制器的设计。然后，通过引入与增强标称系统的干扰相关的附加函数来适当地重新定义成本函数，以补偿不匹配干扰的影响。接下来，相关的 Hamilton-Jacobi-Bellman (HJB) 方程的解通过使用神经网络 (NNs) 的权重自适应律在线求解。此外，利用附加的鲁棒化项来补偿神经网络逼近误差的影响，从而保证闭环系统的渐近稳定性。最后利用Lyapunov方法证明闭环系统的所有信号是渐近收敛的。仿真实例证明了所提出方案的有效性。