This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

A survey of iterative learning control

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

In this paper, the iterative learning control (ILC) literature published between 1998 and 2004 is categorized and discussed, extending the earlier reviews presented by two of the authors. The papers includes a general introduction to ILC and a technical description of the methodology. The selected results are reviewed, and the ILC literature is categorized into subcategories within the broader division of application-focused and theory-focused results.

Iterative Learning Control: Brief Survey and Categorization

Model-based iterative learning control with a quadratic criterion for time-varying linear systems

In this chapter we give an overview of the field of iterative learning control (ILC). We begin with a detailed description of the ILC technique, followed by two illustrative examples that give a flavor of the nature of ILC algorithms and their performance. This is followed by a topical classification of some of the literature of ILC and a discussion of the connection between ILC and other common control paradigms, including conventional feedback control, optimal control, adaptive control, and intelligent control. Next, we give a summary of the major algorithms, results, and applications of ILC given in the literature. This discussion also considers some emerging research topics in ILC. As an example of some of the new directions in ILC theory, we present some of our recent results that show how ILC can be used to force a desired periodic motion in an initially non-repetitive process: a gas-metal arc welding system. The chapter concludes with summary comments on the past, present, and future of ILC.

Iterative Learning Control: An Expository Overview

An algorithm for iterative learning control is proposed based on an optimisation principle used by other authors to derive gradient-type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realisation in terms of Riccati feedback and feedforward components. This realisation also has the advantage of implicitly ensuring automatic step-size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants. One important feature of the proposed algorithm is the dependence of the speed of convergence on weight parameters appearing in the norms of the signals chosen for the optimisation problem.

Iterative learning control for discrete-time systems with exponential rate of convergence

An algorithm for iterative learning control is developed on the basis of an optimization principle which has been used previously to derive gradient-type algorithms. The new algorithm has numerous benefits which include realization in terms of Riccati feedback and feedforward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm is expressed as a very general norm optimization problem in a Hilbert space setting and hence, in principle, can be used for both continuous and discrete time systems. A basic relationship with almost singular optimal control is outlined. The theoretical results are illustrated by simulation studies which highlight the dependence of the speed of convergence on parameters chosen to represent the norm of the signals appearing in the optimization problem.

Iterative learning control using optimal feedback and feedforward actions

A new optimization-based iterative learning control algorithm is proposed and its properties derived. An important characteristic of this algorithm is that it uses present and future predicted errors to compute the current control, in a similar manner to model-based predictive control using a receding horizon. In particular, it enables the algorithm designer to achieve good control over convergence rate. The actual implementation has a multimodel structure but uses standard linear quadratic regulator methods for a causal formulation (in the iterative learning sense) of what is originally a non-causal algorithm. The results are illustrated by simulations.

Predictive optimal iterative learning control

A new design methodology for iterative learning control systems is developed. It is based on the convergence condition for systems operating on an infinite time interval which is of the H∞ type. The principal idea of the design technique is to design a learning controller such that the speed of convergence is maximized, with a compromise to robustness. The issue of finite versus infinite trial lengths is addressed, as well as limitations on the best achievable rate of convergence due to structural properties of the plant.

An H∞ approach to linear iterative learning control design

An algorithm for iterative learning control is proposed based on an optimization principle used by other authors to derive gradient type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realization in terms of Riccati feedback and feed-forward components. This realization also has the advantage of implicitly ensuring automatic step size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants which can be arbitrarily changed by design parameters.

N. Amann

Papers

Iterative learning control for discrete-time systems with exponential rate of convergence

Iterative learning control using optimal feedback and feedforward actions

Predictive optimal iterative learning control

An H∞ approach to linear iterative learning control design

Iterative learning control for discrete time systems using optimal feedback and feedforward actions