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ABSTRACT Model‐free iterative learning control (ILC) can lead to high performance by attenuating repeating disturbances completely, using dedicated experiments on the real system to replace the traditional model. The aim of this paper is to develop a fast data‐driven method for MIMO ILC that uses random learning in the form of efficient unbiased gradient estimates. This is achieved by developing a stochastic conjugate gradient algorithm, in which the search direction and optimal step size are generated using dedicated experiments. The approach is applied to MIMO automated feedforward tuning. Simulation and experimental results show that the method is superior to earlier stochastic and deterministic methods. [ABSTRACT FROM AUTHOR]

Summary In this article, for non‐parameterized nonlinear continuous (NPNC) multiple‐input multiple‐output (MIMO) systems, two combined iteration‐domain and time‐domain adaptive iterative learning control (ILC) algorithms are proposed to track iteration‐varying reference trajectories repetitively over a finite time interval. Different from the general requirement in adaptive control community that the control gain matrices of the controlled systems are real symmetric and positive‐definite, only the nonsingular property of the control gain matrices is assumed. Moreover, there are just two adaption parameters and one adaption parameter involved in the proposed two adaptive ILC algorithms respectively such that the computation load and memory‐space are greatly saved. A simulation example is utilized to illustrate the effectiveness of the two proposed adaptive ILC algorithms with less adaption parameters. [ABSTRACT FROM AUTHOR]

Summary In this paper, an iterative learning‐based spatiotemporal fault estimation issue in switched reaction–diffusion systems is investigated. Initially, average dwell‐time switching rules are utilized to describe a class of switched reaction–diffusion systems characterized by mode jumps. Then, different from the existing fault estimation methods, a fault estimator is designed for spatiotemporal faults to realize an accurate estimation of faults by using the iterative learning strategy. Subsequently, to improve the speed of fault estimation, an adaptive iterative learning‐based fault estimation law is proposed, which can achieve faster fault estimation by continuously adjusting the iterative learning gain. Moreover, sufficient conditions for the convergence of the fault estimation error are obtained by using the λ$$ \lambda $$‐norm and the mathematical induction methods. Finally, an illustrative example is presented to check the practicality and superiority of the proposed fault estimation scheme. [ABSTRACT FROM AUTHOR]

Summary: The initial state inconsistency and iteration‐varying trajectory problems are considered in adaptive iterative learning control (AILC) to enhance the tracking performance of the non‐strict feedback systems with unknown input nonlinearities. Through constructing an error reference trajectory independence of the reference signal, the restrictions on the initial condition and reference trajectory are both relaxed. Subsequently, a backstepping‐based AILC methodology is systematically presented to ensure that the error reference trajectory can be followed by the actual tracking error. Integral Lyapunov functions are employed to design the recursive controllers, avoiding potential singularity problems resulting from the differentiation of gain functions. Rigorous analysis is provided without imposing constraints on the control gain functions to demonstrate tracking error convergence. Numerical simulations are included to illustrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: Data losses and noises in both forward and feedback channels significantly impact the convergence of networked iterative learning control (ILC) systems. To address this issue, this article considers a class of linear time‐invariant objects controlled by proportional ILC controllers, an optimal state filter is then designed at the ILC controller side that aims to guarantee the convergence of the input transmitted by ILC controllers. First, two data transmission processes are introduced to account for the effects of data losses and noises. Second, a filtering model is established utilizing only the object information and the aforementioned data transmission processes. Third, the optimal state filter is designed on the basis of the orthogonal projection principle. This filtered state facilitates the acquisition of actual output errors, thus improving the convergence of the input transmitted by ILC controllers. Simulation results demonstrate the effectiveness of the proposed state filters. [ABSTRACT FROM AUTHOR]

Summary: In this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with H∞$$ {H}_{\infty } $$ performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we develop an online learning algorithm for solving the Bellman equation for affine in the control discrete‐time nonlinear uncertain dynamical systems. To ensure accelerated learning of our algorithm in generating optimal control policies, we use an actor‐critic structure predicated on higher‐order tuner laws. More specifically, we construct a Nesterov‐like architecture involving momentum‐based learning laws leading to an accelerated convergence of the optimal control policy. The proposed online learning‐based optimal control framework guarantees uniform ultimate boundedness of the closed‐loop system under the assumption that the system is persistently excited. Finally, two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: In this article, we give an alternative representation and prior estimation of solution to delayed linear discrete systems with a second‐order difference with the help of the notation of delayed discrete matrix functions via their norm estimations. As an application, this solution is used to study iterative learning control under the suitable updating laws and sufficient conditions to guarantee that asymptotic convergence tracking results are presented. Finally, two numerical examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the identification problem of an output‐error nonlinear system with saturation and dead‐zone nonlinearity. Introducing a switching function and by means of the auxiliary model identification idea, an auxiliary model hierarchical least squares‐based iterative algorithm is proposed for estimating the parameters of the nonlinear system. Based on the hierarchical identification model, an auxiliary model hierarchical gradient‐based iterative algorithm is presented for the nonlinear system by utilizing the gradient search. In order to take full advantage of the system data, an auxiliary model hierarchical multi‐innovation gradient‐based iterative algorithm is derived for the nonlinear system according to the multi‐innovation identification theory. Finally, the numerical simulation results illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: The design of tracking control problem and compensation of disturbance for switched neutral systems with multiple time‐delays and external disturbances are addressed in this paper. In this regard, a modified repetitive control technique based on the Matausek‐Micic modified Smith predictor approach is being implemented, which assures the exact tracking performance and disturbance attenuation with high precision in the considered system. To be specific, the integration of transfer function with modified Smith predictor block not only provides the accurate compensation of input time‐delays but also ensures the exact estimation and attenuation of external disturbances effectually. Furthermore, according to Lyapunov stability approach combined with average‐dwell‐time technique, a group of adequate conditions is derived in the form of matrix inequalities. Simultaneously, by solving the established matrix inequalities using available software the controller gain matrices are calculated. Ultimately, the simulation results of three numerical examples are presented to validate the efficiency and dominance of the suggested control procedure. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the parameter estimation issues of multivariate equation‐error autoregressive moving average systems. By applying the gradient search and the multi‐innovation theory, we derive a multi‐innovation gradient based iterative (MI‐GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F‐D‐GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input‐output data and to transform an original system into several subsystems. Compared with the MI‐GI algorithm, the F‐D‐GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

With the assistance of reliable control technique, the nonfragile tracking problem has been proposed in this paper for a class of switched systems with external disturbances under the aegis of modified repetitive controller. Notably, the designed repetitive controller is used to improve the tracking performance of the addressed switched systems. Preciously, the influence of external disturbances are estimated through the improved equivalent‐input‐disturbance strategy, wherein the effect caused by the external disturbances to the output channel are reduced by the aid of modified repetitive control strategy. The fundamental intention of this control synthesis is that the output of the system precisely tracks the reference signal even in the presence of external disturbances and gain fluctuations. For that cause, Lyapunov stability technique in conjunction with average dwell time approach is implemented to obtain adequate conditions in the shape of linear matrix inequalities which insists the exponential stability for the addressed system. Ultimately, the efficiency and supremacy of the proposed control schemes are justified via two numerical examples, wherein it is exposed to view that the developed control strategy is capable of good tracking performance and also estimates the external disturbances efficiently. [ABSTRACT FROM AUTHOR]

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]

Summary: This article presents a PI‐type iterative learning control (ILC) law with initial state learning for a class of α$$ \alpha $$ (0<α≤1$$ 0<\alpha \le 1 $$) fractional order two‐dimensional (2D) linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally 2−α$$ 2-\alpha $$ order accuracy. Then, a PI‐ILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A linear matrix inequality‐based sufficient condition is derived to guarantee that the tracking error is asymptotically convergent. The obtained convergence condition is fractional order dependent. Most of the classical ILC conditions for fractional order one‐dimensional linear systems fall into the special cases of this article. Finally, the simulation results show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Summary: In recent years, multi‐agent system (MAS) have attracted extensive attention, but the study for MAS via zonotope theory is very few. This article considers the distributed cooperative fault detection (FD) and fault isolation (FI) problems for a MAS, in which every agent is assumed to be with disturbances in both the sate equation and output equation, by combining Luenberger‐like observers and zonotope theory. To begin with, a robust H∞ observer is constructed for each agent, and zonotope theory is applied on the error dynamic system of the H∞ observer such that the boundary estimation of the system state can be computed iteratively when the MAS has no fault. After this, for distributed cooperative FD purpose, a residual is also constructed based on the H∞ observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation of the residual is calculated by using zonotope method, and based on the residual interval estimate, a residual‐based distributed cooperative FD strategy is presented. Moreover, the distributed cooperative FI scheme is discussed and an FI strategy is also developed by modifying the distributed cooperative FD scheme. Finally, a simulation example is presented to show the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: We introduce an impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices whose solution is given by delayed perturbation of Mittag–Leffler type matrix function. The existence and uniqueness of the solution of the system is proved by using Banach contraction principle. The Ulam–Hyers stability of the given system below are demonstrated. Construct the iterative learning control (ILC) problem obtaining from the mentioned system. The conditions of convergence of ILC problem of each of P, D, and Dα‐types are presented and proved. A comprehensive example with three different original reference trajectories is given to illustrate some theoretical results. This article provides novel outcomes. [ABSTRACT FROM AUTHOR]

This article proposes an effective iterative learning control (ILC) approach based on successive projection scheme for repetitive systems with randomly varying trial lengths. A modified ILC problem is formulated to extend the classical ILC task description to incorporate a randomly varying trial length, while its design objective considers themathematical expectation of its tracking error to evaluate the task performance. To solve this problem, this article employs the successive projection framework to give an iterative input signal update law by defining the corresponding convex sets based on the design requirements. This update law further yields an ILC algorithm, whose convergence properties are proved to be held under mild conditions. In addition, the input signal constraint can be embedded into the design without violating the convergence properties to obtain an alternative algorithm. The performance of the proposed algorithms is verified using a numericalmodel to show the effectiveness at occasionswith and without input constraints. [ABSTRACT FROM AUTHOR]

Summary: Initial condition problem is crucial to a conventional iterative learning control (ILC) scheme, which steers the tracking error from arbitrary initial value to zero in the time steps equaling to the relative degree of the system undertaken. The implementation may be difficult, due to the practical limitation for the control amplitude. This paper presents an error‐tracking approach to discrete‐time adaptive ILC designs for tracking nonidentical tasks in the presence of initial repositioning errors, which may be quite large. A prototype iterative learning algorithm is derived for estimating the time‐varying unknowns, and the saturation is introduced for assuring the estimates to keep away from zero. A key technical lemma, tailored for the analysis purpose in the iteration domain, is presented and applied to analysis of the ILC scheme. The tracking performance of the closed‐loop system is evaluated and explored in detail. It is shown that the perfect tracking for the error between the tracking error and the desired error is achieved at every time instant, while the input and output signals remain bounded. By the simulation example, the proposed scheme is verified to be applicable to tracking tasks without restriction on initial repositioning. [ABSTRACT FROM AUTHOR]

Summary: In this article, an observer‐based adaptive boundary iterative learning control law is developed for a class of two‐link rigid‐flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control. [ABSTRACT FROM AUTHOR]

Summary: Recently proposed adaptive dynamic programming (ADP) tracking controllers assume that the reference trajectory follows time‐invariant exo‐system dynamics—an assumption that does not hold for many applications. In order to overcome this limitation, we propose a new Q‐function that explicitly incorporates a parametrized approximation of the reference trajectory. This allows learning to track a general class of trajectories by means of ADP. Once our Q‐function has been learned, the associated controller handles time‐varying reference trajectories without the need for further training and independent of exo‐system dynamics. After proposing this general model‐free off‐policy tracking method, we provide an analysis of the important special case of linear quadratic tracking. An example demonstrates that our new method successfully learns the optimal tracking controller and outperforms existing approaches in terms of tracking error and cost. [ABSTRACT FROM AUTHOR]

Summary: An observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein. [ABSTRACT FROM AUTHOR]

Summary: This paper is a generalization of the recently developed techniques of initial excitation (IE)–based adaptive control with an introduction to the definition of semi‐initial excitation (semi‐IE), a still more relaxed notion than IE. Classical adaptive controllers typically ensure Lyapunov stability of the extended error dynamics (tracking error + parameter estimation error) and asymptotic tracking, while requiring a stringent condition of persistence of excitation (PE) for parameter convergence. Of late, the authors have proposed a new adaptive control architecture, which guarantees parameter convergence under the online‐verifiable IE condition leading to exponential stability of the extended error dynamics. In earlier works, it has been established that the IE condition is significantly milder than the classical PE condition. The current work further slackens the excitation condition by proposing the concept of semi‐IE. The proposed adaptive controller is proved to ensure convergence of the parameter estimation error to a lower‐dimensional manifold under the weaker semi‐IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed algorithm is shown to improve transient response of tracking error sufficiently in contrast to conventional adaptive controllers. [ABSTRACT FROM AUTHOR]

Summary: An adaptive‐optimal control architecture is presented for adaptive control of constrained aerospace systems with matched uncertainties that are subject to dynamic stochastic change. The architecture brings together three key elements, ie, model predictive control–based reference command shaping, Gaussian process (GP)–based Bayesian nonparametric model reference adaptive control (MRAC), and online GP clustering over nonstationary GPs. Model predictive control optimizes reference model and its shaped output is passed into GP–based MRAC, which is used to learn the model in presence of significant time‐varying stochastic uncertainty while maintaining stability. Based on a likelihood ratio test, the changepoints are detected and learned. Lastly, the models are created and clustered by non‐Bayesian clustering algorithm. The key salient feature of our architecture is that not only can it detect changes but also it uses online GP clustering to enable the controller to utilize past learning of similar models to significantly reduce learning transients. Furthermore, persistence of excitation conditions are significantly relaxed due to the use of GP‐MRAC. Stability of the architecture is argued theoretically and performance is validated empirically on different scenarios for wing rock dynamics. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we develop an adaptive control algorithm for addressing security for a class of networked vehicles that comprise a formation of n^ human‐driven vehicles sharing kinematic data and an autonomous vehicle in the aft of the vehicle formation receiving data from the preceding vehicles through wireless vehicle‐to‐vehicle communication devices. Specifically, we develop an adaptive controller for mitigating time‐invariant state‐dependent adversarial sensor and actuator attacks while guaranteeing uniform ultimate boundedness of the closed‐loop networked system. Furthermore, an adaptive learning framework is presented for identifying the state space model parameters based on input‐output data. This learning technique utilizes previously stored data as well as current data to identify the system parameters using a relaxed persistence of excitation condition. The effectiveness of the proposed approach is demonstrated by an illustrative numerical example involving a platoon of connected vehicles. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on solving the adaptive optimal tracking control problem for discrete‐time linear systems with unknown system dynamics using output feedback. A Q‐learning‐based optimal adaptive control scheme is presented to learn the feedback and feedforward control parameters of the optimal tracking control law. The optimal feedback parameters are learned using the proposed output feedback Q‐learning Bellman equation, whereas the estimation of the optimal feedforward control parameters is achieved using an adaptive algorithm that guarantees convergence to zero of the tracking error. The proposed method has the advantage that it is not affected by the exploration noise bias problem and does not require a discounting factor, relieving the two bottlenecks in the past works in achieving stability guarantee and optimal asymptotic tracking. Furthermore, the proposed scheme employs the experience replay technique for data‐driven learning, which is data efficient and relaxes the persistence of excitation requirement in learning the feedback control parameters. It is shown that the learned feedback control parameters converge to the optimal solution of the Riccati equation and the feedforward control parameters converge to the solution of the Sylvester equation. Simulation studies on two practical systems have been carried out to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: Concurrent learning (CL) is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral CL method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. Data recorded online is exploited in the adaptive update law, and numerical integration is used to circumvent the need for state derivatives. The novel adaptive update law results in negative definite parameter error terms in the Lyapunov analysis, provided an online‐verifiable finite excitation condition is satisfied. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation. The result is also extended to Euler‐Lagrange systems, and simulations on a two‐link planar robot demonstrate the improved performance compared to gradient‐based adaptation laws. [ABSTRACT FROM AUTHOR]

Summary: This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous‐time dynamical systems and discrete‐time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning‐based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous‐time dynamical systems and discrete‐time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems. [ABSTRACT FROM AUTHOR]

Summary: Iterative learning control (ILC) is a family of digital control concepts, which can be used for a large variety of different applications. Each application has its own properties like sampling time and storage needs. This paper shows two real‐time ILC applications with different time scales and storage demands. First, the cavities of one of the world's leading pulsed free‐electron laser are controlled by a norm‐optimal ILC using only the information about the last pulse but with sample times below microseconds. Second, a heating system is controlled by a data‐driven ILC with a sample time in the range of minutes but using all available historic data sets of past trials. Tensor decomposition methods for storage demand and complexity reduction are applied to both applications, which results in a norm‐optimal tensor ILC, as well as, a data‐driven tensor ILC, although the time constants for the two applications vary by eight orders of magnitude. [ABSTRACT FROM AUTHOR]

Summary: Robust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined L1 adaptive control and iterative learning control (ILC) framework to achieve high‐precision trajectory tracking in the presence of unknown and changing disturbances. The L1 adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses L1 adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high‐level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined L1‐ILC framework compared with approaches using ILC with an underlying proportional‐derivative controller or proportional‐integral‐derivative controller. Results highlight that our L1‐ILC framework can achieve high‐precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an iterative learning estimator is proposed to deal with period intermittent fault estimation problem in a class of nonlinear uncertain systems. First, state observer is designed for state reconstruction, followed by the Lyapunov function is presented to guarantee the convergence of the system output. Then, the iterative learning scheme–based fault estimator is presented to track the fault signal and the optimal function is established to ensure tracking error convergence. Moreover, linear matrix inequalities and Schur complements are utilized to obtain the sufficient conditions for the existence of iterative learning estimator. Compared with the existing results, error augmented systems should not satisfy the strictly positive realness assumption. Besides, previous state estimation error is used for current fault estimation such that to improve the estimating accuracy. Finally, 2 numerical examples are given to illustrate the effectiveness and validity of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses the iterative learning control problem under random data dropout environments. The recent progress on iterative learning control in the presence of data dropouts is first reviewed from 3 aspects, namely, data dropout model, data dropout position, and convergence meaning. A general framework is then proposed for the convergence analysis of all 3 kinds of data dropout models, namely, the stochastic sequence model, the Bernoulli variable model, and the Markov chain model. Both mean square and almost sure convergence of the input sequence to the desired input are strictly established for noise-free systems and stochastic systems, respectively, where the measurement output suffers from random data dropouts. Illustrative simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ-type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively from both theoretical and practical viewpoints. These schemes include the original adaptive scheme, projection-based scheme, smooth function-based scheme and its alternative, and dead-zone-like scheme. The consensus convergence and constraints guarantee are strictly proved for each control scheme by using the barrier composite energy function approach. Illustrative simulations verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper presents a stability analysis of the iterative learning control for discrete-time systems with data quantization. Three quantized iterative learning control schemes are considered by using different quantized signals, including system output quantized signal, tracking error quantized signal, and control input quantized signal. The logarithmic quantizer is introduced to decode these signals with a number of quantization levels, and the sector bound method is used to deal with the quantization error. Based on the supervector formulation for iterative learning control systems, some convergence conditions for these iterative learning control laws are given, respectively. It is shown that iterative learning control laws with system output quantized signal and control input quantized signal only guarantee that the tracking error converges to a bound and the bound depending on quantization density and desired trajectory. Thus, the iterative learning control law with tracking error quantized signal can obtain zero tracking error. These results are illustrated by 2 examples. [ABSTRACT FROM AUTHOR]

In this work, we present a novel iterative learning control (ILC) scheme for a class of joint position constrained robot manipulator systems with both multiplicative and additive actuator faults. Unlike most ILC literature that requires identical reference trajectory from trail to trail, in this work the reference trajectory can be non-repetitive over the iteration domain without assuming the identical initial condition. A t a n-type Barrier Lyapunov Function is proposed to deal with the constraint requirements which can be both time and iteration varying, with ILC update laws adopted to learn the iteration-invariant system uncertainties, and robust methods used to compensate the iteration and time varying actuator faults and disturbances. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraint requirements on the joint position vector will not be violated during operation. An illustrative example on a two degree-of-freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional-derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider the design problem of making the convergence of the bounded-input, multi-input iterative learning controller presented in our previous work robust to errors in the model-based value of the input-output Jacobian matrix via a minimax (min-max or 'minimize the worst case') approach. We propose to minimize the worst case (largest) value of the infinity-norm of the matrix whose norm being less then unity implies convergence of the controller. This matrix is the one associated with monotonicity of a sequence of input error norms. The input-output Jacobian uncertainty is taken to be an additive linear one. Theorem 3.1 and its proof show that the worst-case infinity-norm is actually minimized by choosing either the inverse of the centroid of the set of possible input-output Jacobians or a zero matrix. And an explicit expression is given for both the criteria used to choose between the two matrices and the resulting minimum worst-case infinity norm. We showed previously that the matrix norm condition associated with monotonicity of a sequence of output-error norms is not sufficient to assure convergence of the bounded-input controller. The importance of knowing which norm condition is the relevant one is demonstrated by showing that the set of minimizers of the minimax problem formulated with the wrong norm does not contain in general minimizers of the maximum relevant norm and moreover can lead to a gain matrix that destroys the assured convergence of the bounded-input controller given in previous work. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers iterative learning control for a class of uncertain multiple-input multiple-output discrete linear systems with polytopic uncertainties and actuator faults. The stability theory for linear repetitive processes is used to develop control law design algorithms that can be computed using linear matrix inequalities. A class of parameter-dependent Lyapunov functions is used with the aim of enlarging the allowed polytopic uncertainty range for successful design. The effectiveness and feasibility of the new design algorithms are illustrated by a gantry robot case study. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new robust adaptive iterative learning control approach is proposed for discrete-time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well-designed dead-zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function-based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration-varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single-link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative learning control (ILC) scheme based on an iteratively moving average operator for nonlinear dynamic systems with randomly varying trial lengths. By using the iteratively moving average operator, the proposed ILC algorithm overcomes the limitation of traditional ILC that all trial lengths must be identical. It is shown that for nonlinear affine and non-affine systems, the proposed learning algorithm works effectively to nullify the tracking error. In the end, two illustrative examples are presented to demonstrate the performance and the effectiveness of the proposed ILC scheme for nonlinear dynamic systems. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a novel neural network based terminal iterative learning control method is proposed for a class of uncertain nonlinear non-affine systems to track run-varying reference point with initial state variance. In this new control scheme, the non-affine terminal dynamics are converted affine, and the unrealisable recurrent network is simplified into realisable static network. As a result, the effect of initial state and control signal on terminal output can be estimated by neural network. With this estimation, the proposed control scheme can drive nonlinear non-affine systems to track run-varying reference point in the presence of initial state variance. Stability and convergence of this approach are proven, and numerical simulation results are provided to verify its effectiveness. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) is a well-established approach for precision tracking control of systems, which perform a repeated tracking task defined over a fixed time interval. Despite a rich theoretical framework accompanied by a wide array of application studies, comparatively little attention has been paid to the case of multiple input, multiple output (MIMO) systems. Here, the presence of interacting dynamics often correlates with reduced performance. This article focuses on a general class of linear ILC algorithms and establishes links between interaction dynamics and reduced robustness to modeling uncertainty, and slower convergence. It then shows how these and other limitations can be addressed by relaxing the tracking requirement to include only a subset of time points along the time duration. This is the first analysis to show how so-called 'point-to-point' ILC can address performance limitations associated with highly coupled systems. Theoretical observations are tested using a novel MIMO experimental test facility, which permits both exogenous disturbance injection and a variable level of coupling between input and output pairs. Results compare experimental observations with theoretical predictions over a wide range of interaction levels and with varying levels of injected noise. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a model-based nonlinear iterative learning control (NILC) for nonlinear multiple-input and multiple-output mechanical systems of robotic manipulators. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory-tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. Both standard and bounded-error learning control laws with feedback controllers attached are considered. The NILC synthesis is based on a dynamic model of a six degrees of freedom robotic manipulator. The dynamic model includes viscous and Coulomb friction and input generalized torques are bounded. With respect to the bounded-error and standard learning processes applied to a virtual PUMA 560 robot (Unimation, Inc. Danburry, CT, USA), simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, iterative learning control (ILC) of a class of non-affine-in-input processes is considered in Hilbert space, where the plant operators are quite general in the sense that they could be static or dynamic, differentiable or non-differentiable, continuous-time or discrete-time, and so forth. The control problem is first transformed to a problem of solving global implicit function to ensure the uniqueness of desired control input. Then, two contraction mapping-based ILC schemes are proposed in terms of the continuous differentiability of process model, where the learning convergence condition is derived through rigorous analysis. The proposed ILC schemes make full use of the process repetition, deal with system uncertainties easily, and are effective to infinite-dimensional or distributed parameter systems. In the end, the learning controller is applied to the boundary output control of a class of anaerobic digestion process for wastewater treatment. The control efficacy is verified by simulation. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this work, we propose new iterative learning control (ILC) schemes that deal with nonlinear multi-input multi-output systems under alignment condition with nonparametric uncertainties. A major contribution of this work is to remove the classical resetting condition. Another major contribution of this work is to deal with norm-bounded nonlinear uncertainties that satisfy local Lipschitz condition, in particular to deal with nonlinear uncertain state-dependent input gain matrix that could be non-square left invertible and local Lipschitzian. Two types of composite energy function are proposed to facilitate the ILC design and property analysis. Through rigorous analysis, we show that the new ILC schemes proposed warrant the asymptotical tracking convergence of system states. In the end, an illustrative example is provided to demonstrate the efficacy of the proposed ILC scheme. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete-time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well-known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete-time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed-loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

No abstract is available for this article. [ABSTRACT FROM AUTHOR]