Zhang Huaguang, Cui Lili, Zhang Xin, Luo Yanhong
School of Information Science and Engineering, Northeastern University, Shenyang 110004, China.
IEEE Trans Neural Netw. 2011 Dec;22(12):2226-36. doi: 10.1109/TNN.2011.2168538. Epub 2011 Oct 13.
In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.
本文采用自适应动态规划（ADP）方法，针对未知的一般非线性系统提出了一种新颖的数据驱动鲁棒近似最优跟踪控制方案。在控制器设计中，仅需要可用的输入输出数据，而无需已知的系统动态模型。通过递归神经网络（NN）建立数据驱动模型，利用可用的输入输出数据重构未知的系统动态。通过添加一个与建模误差相关的新颖可调项，首先保证所得建模误差收敛到零。然后，基于所获得的数据驱动模型，利用ADP方法设计近似最优跟踪控制器，该控制器由稳态控制器和最优反馈控制器组成。此外，还设计了一个鲁棒项来补偿实施ADP方法时引入的神经网络近似误差。基于李雅普诺夫方法，对闭环系统进行稳定性分析，结果表明所提出的控制器保证系统状态渐近跟踪期望轨迹。此外，还证明了所获得的控制输入在一个小范围内接近最优控制输入。最后，通过两个数值例子验证了所提控制方案的有效性。
