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The present work aims at investigating the adaptive iterative learning control (AILC) design for uncertain high‐order fully actuated nonlinear systems. In order to show the design principles, three types of nonlinear systems are considered, including systems with just parametric uncertainty, systems with both parametric and input distribution uncertainties as well as systems with both parametric uncertainty and an unknown control gain matrix. For different systems, the corresponding AILC schemes are proposed with different techniques in dealing with various system uncertainties, for which the convergence analysis are conducted rigorously based on the composite energy function. The effectiveness of the proposed AILC strategies is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

In this work, a novel adaptive event‐trigered iterative learning control (ILC) scheme is designed for discrete‐time nonlinear systems with time‐varying parameters and random initial states. The reference trajectory can be iteration‐invariant or iteration‐varying. The control input is updated when the event‐triggering condition is satisfied, which reduces the action time of controller and consequently the unnecessary waste of communication resource. An adaptive event‐triggering condition parameter is designed to improve the efficiency of the event generator. Moreover, the parameter updating law of adaptive iterative learning controller is designed based on the recursive least squares algorithm. With the proposed adaptive ILC with event‐triggered mechanism, the learning convergence along the iteration axis is guaranteed and communication burden is reduced. Finally, rigorous theoretical analysis under Lyapunov theory and illustrative examples are given to demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, for nonlinear continuous non‐parameterized (NCNP) systems, an adaptive iterative learning control (ILC) algorithm, which can adjust the adaptive parameters in both iteration‐domain and time‐domain, is first proposed to track different reference trajectories repetitively over a finite time interval. As the NCNP system is required to asymptotically track reference trajectory in infinite time‐domain, by virtue of partitioning the reference trajectory and system signals with a fixed time interval, the proposed adaptive ILC controller is then extended to handle the asymptotic tracking issue in infinite time‐domain. Therefore, a unified adaptive control approach is practically presented for NCNP systems to track reference trajectories in different domains (the infinite iteration‐domain and the infinite time‐domain). A prominent feature of the unified adaptive control approach is that the unknown control gain matrices in the NCNP systems are assumed to be invertible only. As a result, the general requirement in conventional adaptive control and adaptive ILC that the control gain matrices of plants are real symmetric and positive‐definite (or negative‐definite) is greatly relaxed. In addition, only three adaptive variables are designed for adjusting or updating in the proposed unified adaptive control approach such that the structure of controller is very simple and the memory space for computing is saved. [ABSTRACT FROM AUTHOR]

Summary: This paper is devoted to tracking control of nonlinear multiple‐input multiple‐output systems subject to unknown state delays and non‐repetitive uncertainties. An adaptive iterative learning control scheme is proposed by integrating a P‐type feedback term, an iterative updating term and an additional compensation term. Among these terms, the first one is to alleviate the ill effect caused by non‐repetitive uncertainties and the third one is utilized to handle the unwell learned part. The composite energy function methodology is employed to elaborate the bounded convergence of the tracking error. The validity of the proposed method is compared with existing results via simulation studies. [ABSTRACT FROM AUTHOR]

In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete‐time nonlinear systems with random initial condition, unknown time‐varying input gain and multiple time‐iteration‐varying factors including multiple unknown time‐iteration‐varying parameters and unknown time‐iteration‐varying external disturbance. The iteration‐varying factors can be generated by virtue of multiple iteration‐varying high‐order internal models, respectively, where iteration‐varying high‐order internal model means it has iteration‐varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration‐varying high‐order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective. [ABSTRACT FROM AUTHOR]

This paper explores the iterative learning control (ILC) problem for two‐dimensional (2D) multi‐input multi‐output nonlinear parametric systems by taking all nonrepetitive uncertainties of stochastic initial shifts, different tracking tasks and nonuniform trial lengths into consideration. A 2D stochastic variable is defined with Bernoulli stochastic distribution for the first time to handle iteration‐varying trial lengths. The desired output is incorporated into the learning control law as a feedback to compensate the iterative changes of the tracking tasks. An iterative 2D parameter updating law is established using a new defined virtue tracking error to well address the systems uncertainties and varying trial lengths. Consequently, a novel 2D adaptive ILC (2D‐AILC) is presented by incorporating the control law and parameter updating law. The convergence is proved by introducing both the Lyapunov stability principle and the 2D key technique lemma into the repetitive 2D systems even though the dynamic evolution along with two‐dimensional directions makes it more difficult in the mathematic analysis. The simulation study tests the theoretical results: the presented 2D‐AILC scheme can still accomplish a tracking task exactly even though there exist random initial states, nonrepetitive reference trajectories, and iteration‐varying trial lengths. [ABSTRACT FROM AUTHOR]