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中文摘要：
针对P型迭代学习算法对初始偏差和输出误差扰动敏感，以及PD型迭代学习算法容易放大系统噪声，降低系统鲁棒性的问题，研究了具有任意有界扰动及期望输出的重复运行非线性时变系统的PD型迭代学习跟踪控制算法．利用迭代学习过程记忆的期望轨迹、期望控制以及跟踪误差，给出基于变批次遗忘因子的学习控制器设计，并借助λ范数理论和Bellman—Gronwall不等式，讨论保证闭环跟踪系统批次误差有界的学习增益存在的充分必要条件，及分析控制算法的一致收敛性．本算法改善了系统的鲁棒性和动态特性，单关节机械臂的跟踪控制仿真验证了方法的有效性．
英文摘要：
As the P-type iterative learning control algorithm is sensitive to the initial error and the output error disturbance, and the PD-type iterative learning control algorithm can easily amplify the noise and reduce the robustness of the system, a PD-type iterative learning tracking control algorithm for repetitive nonlinear time-varying systems with any desired output and bounded disturbances is investigated. By using the desired trajectory, the desired control and tracking error expectations memorized in the process of iterative learning, the learning controller is designed based on the variable batches of forgetting factors. Based on the λnorm theory and the Bellman-Gronwall inequality, the necessary and sufficient conditions for the existence of the learning gain are discussed, and the uniform convergence of the control algorithm is analyzed to ensure that the batch error of the closed-loop tracking system is bounded. The robustness and the dynamic performance of the system are improved by the algorithm. Simulation on the tracking control of the single-joint robot arm illustrates the effectiveness of the proposed method.
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