In this article, a novel continuous-time optimal tracking controller is proposed for the single-input-single-output linear system with completely unknown dynamics. Unlike those existing solutions to the optimal tracking control problem, the proposed controller introduces an integral compensation to reduce the steady-state error and regulates the feedforward part simultaneously with the feedback part. An augmented system composed of the integral compensation, error dynamics, and desired trajectory is established to formulate the optimal tracking control problem. The input energy and tracking error of the optimal controller are minimized according to the objective function in the infinite horizon. With the application of reinforcement learning techniques, the proposed controller does not require any prior knowledge of the system drift or input dynamics. The integral reinforcement learning method is employed to approximate the Q-function and update the critic network on-line. And the actor network is updated with the deterministic learning method. The Lyapunov stability is proved under the persistence of excitation condition. A case study on a hydraulic loading system has shown the effectiveness of the proposed controller by simulation and experiment.

中文翻译：

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基于学习的动态未知连续线性系统最优跟踪控制器：理论与案例研究

在本文中，针对动态完全未知的单输入单输出线性系统，提出了一种新颖的连续时间最优跟踪控制器。与最优跟踪控制问题的现有解决方案不同，所提出的控制器引入了积分补偿以减少稳态误差并同时调节前馈部分和反馈部分。建立由积分补偿、误差动力学和期望轨迹组成的增强系统，以制定最优跟踪控制问题。在无限视域内根据目标函数最小化最优控制器的输入能量和跟踪误差。随着强化学习技术的应用，建议的控制器不需要任何系统漂移或输入动态的先验知识。采用积分强化学习方法来逼近 Q 函数并在线更新评论家网络。并且使用确定性学习方法更新演员网络。在持续激励条件下证明了Lyapunov稳定性。一个液压加载系统的案例研究通过仿真和实验证明了所提出的控制器的有效性。