Iterative learning control for discrete-time systems with exponential rate of convergence
01 Mar 1996-Vol. 143, Iss: 2, pp 217-224
TL;DR: An algorithm for iterative learning control is proposed based on an optimisation principle used by other authors to derive gradient-type algorithms and has potential benefits which include realisation in terms of Riccati feedback and feedforward components.
Abstract: 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.
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TL;DR: Though beginning its third decade of active research, the field of ILC shows no sign of slowing down and includes many results and learning algorithms beyond the scope of this survey.
Abstract: 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.
2,645 citations
Cites background from "Iterative learning control for disc..."
...The above optimization problem can be solved in a different way leading to a combination of optimal state feedback control and current-iteration ILC [100], [102]....
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...Minimizing the cost criterion with respect to uj+1 [100], [101] yields the optimal Q-filter FIGURE 4 ILC iteration dynamics....
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TL;DR: In this paper, the authors studied the effect of local derivatives on the detection of intensity edges in images, where the local difference of intensities is computed for each pixel in the image.
Abstract: 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:
1,829 citations
01 Nov 2007
TL;DR: 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.
Abstract: 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.
1,417 citations
TL;DR: It is shown that, within the framework of the quadratic-criterion-based ILC (Q-ILC), various practical issues such as constraints, disturbances, measurement noises, and model errors can be considered in a rigorous and systematic manner.
451 citations
Cites background from "Iterative learning control for disc..."
...Amann et al. (1996) transformed (4) to a causal form by borrowing the idea from the solution of the "nite-time quadratic optimal tracking problem....
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...In the unconstrained, deterministic setting, Amann et al. (1996) derived a noncausal input updating law u k "u k~1 #R~1GTQe k (4) from LJ k /Lu k "0, while Lee et al. (1996) obtained u k "u k~1 #(GTQG#R)~1GTQe k~1 (5) which is indeed a rephrasing of (4) in a pure learning form....
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01 Jan 1999
TL;DR: This chapter gives an overview of the field of iterative learning control (ILC), followed by 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.
Abstract: 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.
397 citations
References
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28,888 citations
"Iterative learning control for disc..." refers methods in this paper
...Using e = r Gu gives the tracking error update relationek+1 = (I +GG ) 1ek 8k 0 (17) and the recursive relation for the input evolutionuk+1 = (I +G G) 1(uk +G r) 8k 0 (18) This last relationship is a form of Levenberg-Marquardt [14] or modified Newton iteration which is familiar in the context of numerical analysis [18], particularly the least-squaresfitting of parameters appearing nonlinearly in models, but in this case it is used for a dynamical system....
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...A formal examination of general robustness issues was not included, but the experience in numerical analysis with the related Levenberg-Marquardt method and results of Iterative Learning Control simulations indicate that the algorithmpossesses robustness to a useful degree....
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...Using e = r Gu gives the tracking error update relation ek+1 = (I +GG ) 1ek 8k 0 (17) and the recursive relation for the input evolution uk+1 = (I +G G) 1(uk +G r) 8k 0 (18) This last relationship is a form of Levenberg-Marquardt [14] or modified Newton iteration which is familiar in the context of numerical analysis [18], particularly the least-squaresfitting of parameters appearing nonlinearly in models, but in this case it is used for a dynamical system....
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01 Jan 1994
TL;DR: The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Note: Includes bibliographical references, 3 appendixes and 2 indexes.- Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08
19,881 citations
Book•
01 Jan 1968
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Abstract: From the Publisher:
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
5,667 citations
Additional excerpts
...The controller on the (k + 1)th trial is obtained with vector differential calculus from the required stationarity condition 12 @Jk+1 @uk+1 = GTQek+1 + R(uk+1 uk) = 0 (15) Since R(t) > 0 8t guarantees the existence of the inverse, the optimal control input is uk+1 = uk + R 1GTQek+1 8k 0 (16) The learning controllerR 1GTQ is equivalent to the adjoint operatorG ofGwith respect to the weighted inner products (12) and (13) [13]....
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Book•
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13 Feb 1986
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