This paper explores how to construct an adaptive iteration learning control (AILC) mechanism for a class of discrete-time nonrepetitive systems subject to iteration-varying unknown parameters and unidentical initial condition. Firstly, for the linear discrete-time nonrepetitive systems, by minimizing the discrepancy of the real system outputs from the estimated system outputs, a gradient-type adaptation law is designed to estimate the system lower triangular parameter matrix and the system initial state. Especially, the current parametric estimation is updated by virtue of the input-output data and the previous estimation. Secondly, an AILC mechanism is constructed based on the estimated system lower triangular parameter matrix, where the control input algorithm and the adaptation law are scheduled in an interactive mode. Thirdly, the boundedness of the estimation error between the real system matrix and the estimation one is derived by means of vector norm theory. Based on the boundedness of the estimation error, the robust condition of the proposed AILC is given. Finally, the proposed AILC is investigated for a class of nonlinear affine systems and the corresponding results are captured. Simulation results illustrate the validity and effectiveness of the proposed AILC schemes.

本文探讨了如何为一类具有迭代变化的未知参数和不相同的初始条件的离散时间非重复系统构建自适应迭代学习控制（AILC）机制。首先，对于线性离散时间非重复系统，通过最小化实际系统输出与估计的系统输出之间的差异，设计了一种梯度类型的适应律，以估计系统的下三角参数矩阵和系统的初始状态。特别地，借助于输入-输出数据和先前的估计来更新当前的参数估计。其次，基于估计的系统下三角参数矩阵构造一个AILC机制，其中控制输入算法和自适应律以交互模式进行调度。第三，利用矢量范数理论推导了实系统矩阵与估计一之间的估计误差的有界性。基于估计误差的有界性，给出了所提AILC的鲁棒条件。最后，针对一类非线性仿射系统研究了所提出的AILC，并捕获了相应的结果。仿真结果说明了所提出的AILC方案的有效性和有效性。