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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]

This paper first investigates robust tracking problem of a high-order iterative learning control (HOILC) algorithm for two classes of two-dimensional linear discrete time-varying Fornasini–Marchesini systems (2-D LDTVFMS) and 2-D LDTVFMS with input delays with iteration-dependent reference trajectory described by a high-order internal model (HOIM) operator, boundary states and disturbances. An extended high-order linear discrete inequality is proposed to guarantee the ILC tracking error of 2-D LDTVFMS converge robustly to a bounded range, the bound of which is relied on iteration-dependent uncertainties from reference trajectory, boundary states and disturbances. A simulation example on a practical thermal process is used to validate the effectiveness and feasibility of the proposed HOILC law. Additionally, it is verified by theory analysis and simulation that no matter how the ILC controller gain is selected, the convergence condition in Theorem 2 of Wan and Li [(2021). High-order internal model based iterative learning control for 2-D linear FMMI systems with iteration-varying trajectory tracking. IEEE Transactions on Systems Man and Cybernetics: Systems, 51, 1462–1472] is not satisfied. Using the proposed HOILC law, perfect tracking result in Theorem 2 of Wan and Li (2021) can be obtained. [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]

In this paper, convergent property of a saturation-strategy-based iterative learning control (ILC) law is first investigated for a class of two-dimensional linear discrete first Fornasini–Marchesini model (2-D LDFFM) with input saturation. A three-dimensional dynamical process is transformed into a 2-D dynamical process by row scanning approach or column scanning approach. As a result, it is theoretical proved no matter which method is adopted, perfect tracking on the desired reference surface is accomplished by virtue of the 2-D linear inequality theory. Numerical simulation on a practical thermal process is used to illustrate the effectiveness and feasibility of the designed ILC law. In addition, ILC convergence analysis for 2-D LDFFM with input delay and input saturation is discussed. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic system (FLS), which can compensate the loss caused by input saturation. Then, the discrete Nussbaum gain technique is adopted along the iteration axis, which can be embedded to the learning control method to identify the control direction of the system. Finally, based on the nonincreasing Lyapunov-like function, it is proven that the adaptive iterative learning controller can converge asymptotically when the number of iterations tends to infinity, and the system signals always remain bounded in the learning process. A simulation example verifies the feasibility and effectiveness of the learning control method. [ABSTRACT FROM AUTHOR]