Most of adaptive iterative learning control (AILC) algorithms focus on one-dimensional (1-D) systems, rather than two-dimensional (2-D) systems. This brief is first concerned with AILC for 2-D nonlinear discrete time-varying Fornasini-Marchesini system (NDTVFMS) with nonrepetitive reference trajectory under iteration-varying boundary states. By using Lyapunov analysis method, it can guarantee that the ultimate tracking error tends to zero asymptotically, and make all identified parameters and system signals to be bounded as iteration number goes to infinity. Two illustrative examples are used to validate the effectiveness of the designed AILC approach.

中文翻译：

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具有迭代变化边界状态的二维非线性离散时变 Fornasini-Marchesini 系统跟踪非重复轨迹的自适应 ILC

大多数自适应迭代学习控制 (AILC) 算法专注于一维 (1-D) 系统，而不是二维 (2-D) 系统。本简介首先涉及在迭代变化边界状态下具有非重复参考轨迹的二维非线性离散时变 Fornasini-Marchesini 系统 (NDTVFMS) 的 AILC。采用李雅普诺夫分析方法，可以保证最终跟踪误差渐近趋于零，并使所有识别参数和系统信号随着迭代次数趋于无穷大而有界。两个说明性示例用于验证设计的 AILC 方法的有效性。