基于经验重放的部分未知非线性系统在线自适应鲁棒跟踪控制与非对称约束输入

Chong Liu, Yalun Li, Zhongxing Duan, Zhousheng Chu, Zongfang Ma
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摘要

本文利用基于经验重放(ER)技术和纯批判神经网络(NN)的改进型自适应动态编程(ADP)方法,解决了具有非对称约束输入的部分未知非线性系统的鲁棒跟踪问题(RTP)。首先,使用识别器神经网络(INN)来识别系统动态的未知部分。随后,利用跟踪误差和期望轨迹构建一个增强系统,从而将鲁棒跟踪问题(RTP)转化为约束最优控制问题(OCP)。研究证明,所设计的 OCP 控制策略能使跟踪误差最终均匀受限(UUB)。然后,利用 ADP 和唯批判 NN 框架求解推导出的汉密尔顿-雅各比-贝尔曼方程(HJBE)。利用梯度下降算法(GDA)推导出部分 NN 权重调节规律,然后利用 ER 技术和 Lyapunov 稳定性理论对其进行改进,使其不再需要激励持续性(PE)和初始容许控制等条件。此外,利用 Lyapunov 技术证明了系统总状态和 NN 权重的闭环稳定性。最后,通过两个仿真实例证明了所提出的控制方案是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Experience replay based online adaptive robust tracking control for partially unknown nonlinear systems with asymmetric constrained‐input
This article solves the robust tracking problem (RTP) for a type of partially unknown nonlinear systems with asymmetric constrained‐input by utilizing an improved adaptive dynamic programming (ADP) method based on experience replay (ER) technique and critic‐only neural network (NN). Initially, an identifier neural network (INN) is used to identify the unknown part of the system dynamics. Subsequently, the tracking error and the desired trajectory are used to construct an augmented system, so that the robust tracking problem (RTP) is transformed into a constrained optimal control problem (OCP). It is proved that the designed control policy of OCP can make the tracking error to be uniformly ultimately bounded (UUB). Then, using the framework of ADP and critic‐only NN to solve the derived Hamilton–Jacobi–Bellman equation (HJBE). The NN weight regulation law is partially derived by using gradient descent algorithm (GDA) and then is improved by using the ER technique and the Lyapunov stability theory, which no longer need the conditions of persistence of excitation (PE) and the initial admissible control. Besides, the total system states and NN weights are proved to be closed‐loop stable by utilizing the Lyapunov technique. Finally, through two simulation examples, it is demonstrated that the proposed control scheme is effective.
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