ABSTRACT In this work, three nonholonomic dynamic linearisation based adaptive P-, PD-, and PID-type iterative learning control schemes are proposed for nonlinear plants with nonrepetitive uncertainties including the different initial states and the iteration varying desired trajectories. We first linearise a non-affined nonlinear system into a linearly affined data model by developing a nonholonomic dynamic linearisation in iteration domain without assuming that the difference between the control inputs in two consecutive iterations be nonzero. On this basis, three adaptive P-type, PD-type, PID-type ILC methods are proposed, respectively. Moreover, both a projection-based parameter updating law to estimate unknown gradients and an iteration-difference observer to estimate nonlinear uncertainties are developed together. The proposed approaches not only have data-driven property like the traditional PID-type ILC, but also can deal with nonrepetitive uncertainties in initial states, desired trajectories, disturbances and so on, like the traditional adaptive ILC. The effectiveness and applicability of the three methods are confirmed by rigorous derivation and simulations.

中文翻译：

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具有迭代变化不确定性的非线性系统的基于非完整动态线性化的自适应 PID 型 ILC

摘要 在这项工作中，提出了三种基于非完整动态线性化的自适应 P、PD 和 PID 型迭代学习控制方案，用于具有非重复不确定性的非线性设备，包括不同的初始状态和迭代变化的期望轨迹。我们首先通过在迭代域中开发非完整动态线性化将非仿射非线性系统线性化为线性仿射数据模型，而不假设两次连续迭代中的控制输入之间的差异为非零。在此基础上，分别提出了三种自适应P型、PD型、PID型ILC方法。此外，同时开发了用于估计未知梯度的基于投影的参数更新律和用于估计非线性不确定性的迭代差分观测器。所提出的方法不仅像传统的 PID 型 ILC 一样具有数据驱动的特性，而且可以像传统的自适应 ILC 一样处理初始状态、期望轨迹、干扰等的非重复不确定性。这三种方法的有效性和适用性都得到了严格的推导和仿真的证实。