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Summary: This article first investigates robust iterative learning control (ILC) problem of a class of large‐scale interconnected systems, which consist of many subsystems described by two‐dimensional linear discrete first Fornasini–Marchesini systems with iteration‐dependent uncertainties arising from not only boundary states, disturbances, but also reference trajectory. A decentralized P‐type ILC law without any information exchanges with other subsystems is proposed such that the ultimate ILC tracking error of each subsystem can converge to a bounded range, the bound of which depends continuously on the bounds of all iteration‐dependent uncertainties considered. Especially, if these iteration‐dependent uncertainties are convergent progressively along the iteration direction, perfect ILC tracking on 2‐D reference trajectory can be obtained. Additionally, a modified ILC law with compensation technique is used to a class of large‐scale interconnected systems composed of many subsystems represented by two‐dimensional linear discrete second Fornasini–Marchesini systems. Two simulation examples are used to demonstrate the effectiveness and validity of the obtained ILC results. Finally, some comparative discussions are given. [ABSTRACT FROM AUTHOR]

In this article, robust and convergent properties of iterative learning control (ILC) laws are investigated for two kinds of two-dimensional (2-D) linear discrete systems (LDS) in the second Fornasini–Marchesini’s model (FMMII). The iteration-dependent uncertainties in reference trajectories, boundary states, and disturbances are considered in the ILC designs of 2-D FMMII. By virtue of the lifting matrix/vector technique, the ILC processes of two kinds of 2-D FMMII are transformed into 2-D linear inequalities. As a result, robust and convergent conditions are obtained for the proposed ILC laws. It is theoretically proved that by using the proposed ILC laws, under the discussed iteration-dependent uncertainties, the ILC tracking errors of 2-D FMMII can be driven into a residual range, the bound of which is relevant to the bound parameters of uncertainties. In particular, when the iteration-dependent uncertainties of 2-D FMMII are progressively convergent in iteration domain, an accurate tracking to the desired reference trajectory can be realized except at the boundaries. Numerical simulations are used to illustrate the validity and feasibility of the designed ILC laws. [ABSTRACT FROM AUTHOR]

This paper is concerned with iterative learning control (ILC) algorithms for two-dimensional (2-D) linear discrete systems described by the first Fornasini–Marchesini model (FMMI) with iteration-varying reference trajectories/profiles. The variation of reference trajectories in iteration domain is represented by a high-order internal model (HOIM) formula. Robustness and convergence of two types of HOIM-based ILC laws with different boundary conditions are investigated, respectively. A strategy employed in this paper is to reconstruct the HOIM-based ILC process of the 2-D linear FMMI system into a set of 2-D linear inequalities or a 2-D linear Roesser model such that sufficient robustness/convergence conditions of the HOIM-based ILC laws are obtained. Under random boundary conditions, the designed ILC law (9) is capable to drive the ILC tracking error into a bounded range. Moreover, under the HOIM-based boundary conditions, a perfect tracking to the iteration-varying reference trajectories can be achieved by utilizing the proposed ILC law (32). Two simulation examples are given to validate the effectiveness of the two proposed ILC algorithms. [ABSTRACT FROM AUTHOR]