In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete-time nonlinear systems with random initial condition, unknown time-varying input gain and multiple time-iteration-varying factors including multiple unknown time-iteration-varying parameters and unknown time-iteration-varying external disturbance. The iteration-varying factors can be generated by virtue of multiple iteration-varying high-order internal models, respectively, where iteration-varying high-order internal model means it has iteration-varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration-varying high-order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective.

中文翻译：

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具有多次迭代变化高阶内部模型的离散时间非线性系统的自适应迭代学习控制

在这项工作中，针对一类具有随机初始条件、未知时变输入增益和包括多个未知时间迭代在内的多个时间迭代变化因素的一类参数离散时间非线性系统，设计了一种自适应迭代学习控制（AILC）方法。 - 变化的参数和未知的时间迭代变化的外部干扰。迭代变化因子可以分别通过多个迭代变化高阶内部模型产生，其中迭代变化高阶内部模型意味着它具有迭代变化阶数或系数。此外，基于递归最小二乘算法设计了参数更新律。使用基于迭代变化的高阶内部模型设计的 AILC，通过李雅普诺夫理论下严格的理论分析，保证了迭代域中的学习收敛。最后，给出了两个仿真例子来证明所提出的方案是有效的。