Robust Iterative Learning Control against Disturbances and Initialization Errors for Uncertain Plants

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

This paper addresses robust performance analysis and synthesis of lifted system iterative learning control (ILC). By applying the full block S-procedure, sufficient conditions for the robust performance of ILC with both unstructured and structured uncertainty are derived. In the synthesis problem, we consider the design of the learning filter Q for modelinversion based ILC. The problem is reformulated as a convex optimization problem such that the converged tracking error is minimized subject to the monotonic convergence condition. This synthesis approach enables full automation of the ILC design since neither an uncertainty model has to be identified nor a robustness filter has to be chosen. The advantages of this novel robust performance ILC technique are demonstrated on an experimental linear motor test setup.

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

In this paper, we present an iterative learning control (ILC) framework for tracking problems with predefined data points that are desired points at certain time instants. To design ILC systems for such problems, a new ILC scheme is proposed to produce output curves that pass close to the desired points. Unlike traditional ILC approaches, an algorithm will be developed in which the control signals are generated by solving an optimal ILC problem with respect to the desired sampling points. In another word, it is a direct approach for the multiple points tracking ILC control problem where we do not need to divide the tracking problem into two steps separately as trajectory planning and ILC controller. The strength of the proposed formulation is the methodology to obtain a control signal through learning law only considering the given data points and dynamic system, instead of following the direction of tracking a prior identified trajectory. The key advantage of the proposed approach is to significantly reduce the computational cost. Finally, simulation results will be introduced to confirm the effectiveness of proposed scheme.

The proportional-integral-derivative (PID) controller is standard technique for controlling the industrial batch process. However, the parameter tuning and updating of PID controller has been a challenging topic for control engineers especially for the real system having initial state error, state and output disturbances. In this paper, a kind of robust optimal iterative learning control (ILC) scheme is suggested to update the PID gains for the linear system with initial state error, state and output disturbances. The quadratic performance criteria is considered, which constitute of the error and input slew rate, and the robust BIBO stability is investigated theoretically for the proposed PID type ILC scheme. In addition, the bound of the tracking error has been calculated by using Lyapunov composite energy function. Simulation examples are also given to demonstrate the effectiveness of the proposed scheme in term of its ability to deal with linear as well as nonlinear system

In this paper a discrete-time iterative learning controller for single input single output systems is presented. The iterative learning controller works with a reduced sampling rate that ensures the reduction of an appropriate norm of the error trajectory from cycle to cycle and can cope with initial state error. Initial state error occurs when the initial state of the system is different from the initial state that is implicitly given by the reference trajectory. If the initial state changes for every learning iteration, then the controller cannot achieve ideal tracking but the error trajectory is bounded. Using two different sample times together with a potentially time variant learning gain improves the controller performance for dealing with initial state error. Simulation examples are presented to show the results of the proposed iterative learning controller with reduced sampling rate.

SummaryThis 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.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

In this paper is proposed a robust higher-order iterative learning control (ILC) algorithm for discrete-time systems. In contrast to conventional discrete-time learning methods, the proposed learning algorithm is constructed based on both time-domain performance and iteration-domain performance. Also, the proposed learning algorithm use more than one past error in the iteration-domain. It is proved that the proposed method has robustness in the presence of external disturbances and, in absence of all disturbances, the convergence of the proposed learning algorithm is guaranteed. A numerical example is given to show the robustness in the presence of state disturbance and convergence property according to parameters change.

Based on Nesterov accelerated gradient method, the problem of iterative learning control for a class of linear discrete-time systems is considered in this paper. Firstly, the iterative learning control problem of linear discrete-time systems is transformed into an iterative least-squares problem. Then, the Nesterov accelerated gradient method is introduced into the iterative learning control framework. Note that the Nesterov accelerated gradient learning algorithm has the capability of fast convergence. It is shown that the algorithm presented in this paper can guarantee the output tracking error converges to zero with rate O(1/k) , where k is the iteration counter. Moreover, the monotonic convergence of the Nesterov accelerated gradient learning algorithm is analyzed and discussed. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Most of the existing iterative learning control algorithms proposed for time-delay systems are based on the condition that the time-delay is precisely available, and the initial state is reset to the desired one or a fixed value at the start of each operation, which makes great limitation on the practical application of corresponding results. In this paper, a new iterative learning control algorithm is studied for a class of nonlinear system with uncertain state delay and arbitrary initial error. This algorithm needs to know only the boundary estimation of the state delay, and the initial state is updated, while the convergence of the system is guaranteed. Without state disturbance and output measurement noise, the system output will strictly track the desired trajectory after successive iteration. Furthermore, in the presence of state disturbance and measurement noise, the tracking error will be bounded uniformly. The convergence is strictly proved mathematically, and sufficient conditions are obtained. A numerical example is shown to demonstrate the effectiveness of the proposed approach.

This paper is concerned with the variable initial states problem in iterative learning control (ILC) for linear continuous systems. Firstly, the properties of the trajectory of 2-D continuous-discrete Roesser model are analyzed by using Lyapunov's method. Then, for any variable initial states which absolutely converge to the desired initial state, some sufficient conditions in the form of linear matrix inequalities (LMI) are given to ensure the convergence of the PD-type ILC rules. It implies that the ILC rules can be used to achieve the perfect tacking for variable initial states, even if the system dynamic is unknown. Finally, two numerical examples are given to illustrate the perfect tracking performance with exponentially convergent initial states.

An iterative learning-based adaptive disturbance rejection control (ADRC) method is proposed to tackle control issues for three-dimensional (3D) overhead crane. The tracking differentiator (TD) and extended state observer (ESO) are employed to extract desired displacement and estimate system disturbances. A robust iterative learning control (ILC) law is constructed by integrating sliding mode control (SMC) with ILC. The stability of the closed-loop system is proved through Lyapunov stability theory, and simulations are conducted to verify the effectiveness and robustness of the proposed method.

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.