Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control

Cyclic pseudo-downsampled iterative learning control (ILC) has shown advantages to achieve good learning performance for trajectories containing high-frequency components and has been verified on industrial robot application. This scheme is a multirate ILC in nature and downsamples the fast rate signals (with a sampling period T) to slow rate signals (with a sampling period mT) with a ratio m. Then ILC is carried out on the downsampled signals and interpolates its output to a fast rate signal. For the next iteration, ILC scheme downsamples the signals with the same ratio m but at different sampling points with a time shift T. This process is repeated on the iteration axis so that ILC updates the input of all the sampling points once every m cycles. By experiments [Zhang, B., Wang, D., Ye, Y., Zhou, K. and Wang, Y. (2009) ‘Cyclic Pseudo-downsampled Iterative Learning Control for High Performance Tracking’, Control Engineering Practice, 17, 957–965], this scheme has been shown effective and comparisons with other relevant schemes demonstrate its superior performance. In this article, this cyclic pseudo-downsampled ILC scheme is examined analytically and proved mathematically to be stable and robust. Extensions and insights are also established based on the theoretical developments and simulation verification. pseudo-downsampled ILC scheme.     

城市交通区域的迭代学习边界控制

已有的边界控制方法主要是基于模型的反馈控制算法,其实际应用效果受制于模型参数的标定和环境的影响.迭代学习控制以完全跟踪为目标,仅利用较少的模型信息就可以沿迭代轴实现对系统期望输出的完全跟踪.基于城市交通流的重复特性,提出一种城市交通区域的迭代学习边界控制方法,给出跟踪误差收敛性分析.以日本横滨区域为对象分别进行3种场景的仿真:早高峰、晚高峰和中心区域拥堵.仿真结果表明,迭代学习控制方法对于各种场景下的区域路网交通均能达到较为理想的控制效果.     

Newton method based iterative learning control for discrete non-linear systems

Significant progress has been achieved in terms of both theory and industrial applications of iterative learning control (ILC) in the past decade. However, the techniques of solving non-linear ILC problems are still under development. The main result of this paper is a novel non-linear ILC algorithm that utilizes the capability of the Newton method. By setting up links between non-linear ILC problems and non-linear multivariable equations, the Newton method is introduced into the ILC framework. The implementation of the new algorithm allows one to decompose a nonlinear ILC problem into a sequence of linear time-varying ILC problems. Simulations on a discrete non-linear system and a manipulator model display its advantages. Conditions for its semi-local convergence are analysed. Links of ILC with existing non-linear topics are pointed out as ways to construct new non-linear ILC schemes. Potential improvements are discussed for future work.     

Stability of first and high order iterative learning control with data dropouts

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to output measurement data dropouts. It is assumed that data dropout occurs during the data transfers from the plant to the ILC controller, resulting in what is called intermittent ILC. Using the super-vector approach for ILC, the expectation of output error is used to develop conditions for stability of the first order ILC and high order ILC processes. Through the theoretical analysis, it is shown that the convergence of the intermittent ILC is guaranteed although some measurements are missing. The analysis is also supported by numerical examples.     

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.     

间歇过程最优迭代学习控制的发展:从基于模型到数据驱动

本文综述了间歇过程的基于模型的和数据驱动的最优迭代学习控制方法.基于模型的最优迭代学习控制方法需要已知被控对象精确的线性模型,其研究较为成熟和完善,有着系统的设计方法和分析工具.数据驱动的最优迭代学习控制系统设计和分析的关键是非线性重复系统的迭代动态线性化.本文简要综述了基于模型的最优迭代学习控制的研究进展,详细回顾了数据驱动的迭代动态线性化方法,包括其详细的推导过程和突出的特点.回顾和讨论了广义的数据驱动最优迭代学习控制方法,包括完整轨迹跟踪的数据驱动最优迭代学习控制方法,提出和讨论了多中间点跟踪的数据驱动最优点到点迭代学习控制方法,和终端输出跟踪的数据驱动最优终端迭代学习控制方法.进一步,迭代学习控制研究中的关键问题,如随机迭代变化初始条件、迭代变化参考轨迹、输入输出约束、高阶学习控制律、计算复杂性等.本文突出强调了基于模型的和数据驱动的最优迭代学习控制方法各自的特点与区别联系,以方便读者理解.最后,本文提出数据驱动的迭代学习控制方法已成为越来越复杂间歇过程控制发展的未来方向,一些开放的具有挑战性的问题还有待于进一步研究.     

迭代学习控制综述

系统地论述了迭代学习控制的发展和研究现状,包括学习算法及其各种分析方法、与其他控制技术的结合及其应用都作了的总结.重点对迭代学习控制研究的前沿问题:基于频域分析的迭代学习控制、基于2-D理论的迭代学习控制、基于Lyapunov直接法的迭代学习控制、最优化迭代学习控制和采样迭代学习控制进行阐述.最后讨论了目前研究中存在的问题及未来的研究方向.     

Iterative learning control for uncertain systems: Noncausal finite time interval robust control design

In this paper, we present a novel robust Iterative Learning Control (ILC) control strategy that is robust against model uncertainty as given by an additive uncertainty model. The design methodology hinges on ??_∞ optimization, but formulated such that the obtained ILC controller is not restricted to be causal, and inherently operates on a finite time interval. Optimization of the robust ILC (R‐ILC) solution is accomplished for the situation where any information about structure in the uncertainty is discarded, and for the situation where the information about the structure in the uncertainty is explicitly taken into account. Subsequently, the convergence and performance properties of resulting R‐ILC controlled system are analyzed. On an experimental set‐up, we show that the presented R‐ILC control strategy can outperform an existing linear‐quadratic norm‐optimal ILC approach and an existing causal R‐ILC approach based on frequency domain ??_∞ synthesis. Copyright © 2010 John Wiley & Sons, Ltd.     

A generalized iterative learning controller against initial state error

In this paper, the previous results that the performance of iterative learning control (ILC) algorithm can be improved by adding a proportional term and/or an integral term of error in D-type ILC algorithm are generalized using an operator. Then, a sufficient condition for convergence and robustness of the generalized ILC algorithm are investigated against initial state error. As a special case of the operator, a non-linear ILC algorithm is also proposed and it is shown that the effect of initial state error can be reached to zero in a given finite time. It is shown that the bound of error reduction can be effectively controlled by tuning gains of the proposed non-linear ILC algorithm. In order to confirm validity of the proposed algorithms, two examples are presented.     

Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree

In this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.     

Adaptive ILC for tracking non-repetitive reference trajectory of 2-D FMM under random boundary condition

Almost all of the existing research achievements in Iterative Learning Control (ILC) hitherto have been focused on One-Dimensional (1-D) dynamical systems. Few ILC researches are related to Two-Dimensional Fornasini Marchesina Model (2-D FMM). In this paper, an adaptive ILC approach is proposed for 2-D FMM system with non-repetitive reference trajectory under random boundary condition. The proposed adaptive ILC algorithm learns the coefficient matrices of the system and updates the control input iteratively. As the times of iteration goes to infinity, the ILC tracking error outside the boundary tends to zero and all system signals keep bounded in the whole ILC process. Illustrative examples are provided to verify the validity of the proposed adaptive ILC algorithm.     

Stability analysis of discrete-time iterative learning control systems with interval uncertainty

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plant Markov parameters are subject to interval uncertainty. Using the so-called super-vector approach to ILC, vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ILC process. It is shown that the stability of such interval ILC systems can be determined by checking the stability of the system using only the vertex points of the interval Markov parameters.     

Robust optimal design and convergence properties analysis of iterative learning control approaches

In this paper, we address four major issues in the field of iterative learning control (ILC) theory and design. The first issue is concerned with ILC design in the presence of system interval uncertainties. Targeting at time-optimal (fastest convergence) and robustness properties concurrently, we formulate the ILC design into a min-max optimization problem and provide a systematic solution for linear-type ILC consisting of the first-order and higher-order ILC schemes. Inherently relating to the first issue, the second issue is concerned with the performance evaluation of various ILC schemes. Convergence speed is one of the most important factors in ILC. A learning performance index—Q-factor—is introduced, which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ILC schemes. We further explore a key issue: how does the system dynamics affect the learning performance. By associating the time weighted norm with the supreme norm, we disclose the dynamics impact in ILC, which can be assessed by global uniform bound and monotonicity in iteration domain. Finally we address a rather controversial issue in ILC: can the higher-order ILC outperform the lower-order ILC in terms of convergence speed and robustness? By applying the min-max design, which is robust and optimal, and conducting rigorous analysis, we reach the conclusion that the Q-factor of ILC sequences of lower-order ILC is lower than that of higher-order ILC in terms of the time-weighted norm.     

An extended PID type iterative learning control

This paper presents a new iterative learning control (ILC) for discrete-time single-input single-output (SISO) linear time-invariant (LTI) systems. To establish this ILC, the input of the controlled system is modified by using a novel four-parametric algorithm. This algorithm is called the extended proportional plus integral and derivative (EPID) type, since by eliminating the fourth parameter of it one would get to the PID type ILC, therefore PID type ILC is a special case of it. The convergence of the proposed ILC is analyzed and an optimal method is presented to determine its parameters. It is shown that the given ILC has a better performance than the PID-type one. Three illustrative examples are included to demonstrate the effectiveness and the preference of the presented ILC.     

An algebraic approach to iterative learning control

In this paper discrete-time iterative learning control (ILC) systems are analysed from an algebraic point of view. The algebraic analysis shows that a linear-time invariant single-input–single-output model can always represented equivalently as a static multivariable plant due to the finiteness of the time-axis. Furthermore, in this framework the ILC synthesis problem becomes a tracking problem of a multi-channel step-function. The internal model principle states that for asymptotic tracking (i.e. convergent learning) it is required that an ILC algorithm has to contain an integrator along the iteration axis, but at the same time the resulting closed-loop system should be stable. The question of stability can then be answered by analysing the closed-loop poles along the iteration axis using standard results from multivariable polynomial systems theory. This convergence theory suggests that time-varying ILC control laws should be typically used instead of time-invariant control laws in order to guarantee good transient tracking behaviour. Based on this suggestion a new adaptive ILC algorithm is derived, which results in monotonic convergence for an arbitrary linear discrete-time plant. This adaptive algorithm also has important implications in terms of future research work—as a concrete example it demonstrates that ILC algorithms containing adaptive and time-varying components can result in enhanced convergence properties when compared to fixed parameter ILC algorithms. Hence it can be expected that further research on adaptive learning mechanisms will provide a new useful source of high-performance ILC algorithms.     

Optimal <Emphasis Type="Italic">N</Emphasis>-Parametric Type Iterative Learning Control

One of the most important problems in the field of the iterative learning control (ILC) is to design algorithms, in order to achieve a desired convergence rate. In this paper a new type of the ILC algorithm is introduced, which is called N-parametric type ILC with optimal gains. The convergence of the proposed algorithm is analyzed and an optimal design method is presented to determine its gains. The effect of the number of the parameters on the convergence rate of the presented ILC is investigated. It is shown that N parametric type of this ILC has a better performance than the N-1 one. Illustrative simulation examples are given to verify the theoretical analysis.     

Recent Advances in Iterative Learning Control

In this paper we review the recent advances in three sub-areas of iterative learning control (ILC): 1) linear ILC for linear processes, 2) linear ILC for nonlinear processes which are global Lipschitz continuous (GLC), and 3) nonlinear ILC for general nonlinear processes. For linear processes, we focus on several basic configurations of linear ILC. For nonlinear processes with linearILC, we concentrate on the design and transient analysis which were overlooked and missing for a long period. For general classes of nonlinear processes, we demonstrate nonlinear ILC methods based on Lyapunov theory, which is evolving into a new control paradigm.     

Iterative Learning Control of Iteration-Varying Systems via Robust Update Laws with Experimental Implementation

Iterative learning control (ILC) is an efficient way of improving the tracking performance of repetitive systems. While ILC can offer significant improvement to the transient response of complex dynamical systems, the fundamental assumption of iteration invariance of the process limits potential applications. Utilizing abstract Banach spaces as our problem setting, we develop a general approach that is applicable to the various frameworks encountered in ILC. Our main result is that robust invariant update laws lead to stable behavior in ILC systems, where iteration-varying systems converge to bounded neighborhoods of their nominal counterparts when uncertainties are bounded. Furthermore, if the uncertainties are convergent along the iteration axis, convergence to the nominal case can be guaranteed.