This study first investigates robust iterative learning control (ILC) issue for a class of two-dimensional linear discrete singular Fornasini–Marchesini systems (2-D LDSFM) under iteration-varying boundary states. Initially, using the singular value decomposition theory, an equivalent dynamical decomposition form of 2-D LDSFM is derived. A simple P-type ILC law is proposed such that the ILC tracking error can be driven into a residual range, the bound of which is relevant to the bound parameters of boundary states. Specially, while the boundary states of 2-D LDSFM satisfy iteration-invariant boundary states, accurate tracking on 2-D desired surface trajectory can be accomplished by using 2-D linear inequality theory. In addition, extension to 2-D LDSFM without direct transmission from inputs to outputs is presented. A numerical example is used to illustrate the effectiveness and feasibility of the designed ILC law.

中文翻译：

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具有变化边界状态的二维奇异Fornasini–Marchesini系统的鲁棒迭代学习控制

这项研究首先研究了在迭代变化边界状态下一类二维线性离散奇异Fornasini-Marchesini系统（2-D LDSFM）的鲁棒迭代学习控制（ILC）问题。最初，使用奇异值分解理论，推导了二维LDSFM的等效动力学分解形式。提出了一种简单的P型ILC定律，以便可以将ILC跟踪误差驱动到一个残差范围内，该残差范围的边界与边界状态的边界参数有关。特别地，当2-D LDSFM的边界状态满足迭代不变边界状态时，可以通过使用2-D线性不等式理论来实现对2-D所需表面轨迹的精确跟踪。此外，还提出了对二维LDSFM的扩展，而无需从输入到输出的直接传输。