Analysis of Linear Iterative Learning Control Schemes -A 2D Systems/Repetitive Processes Approach
01 Apr 2000-Multidimensional Systems and Signal Processing (Kluwer Academic Publishers)-Vol. 11, Iss: 1, pp 125-177
TL;DR: Results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the branch of 2D linear systems known as linear repetitive processes are developed.
Abstract: This paper first develops results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the branch of 2D linear systems known as linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results, in the form of fundamental limitations on the benefits of using this law, are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics of the example under consideration. Following this, previously reported powerful 2D predictive and adaptive control algorithms are reviewed. Finally, new iterative adaptive learning control laws which solve iterative learning control algorithms under weak assumptions are developed.
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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
Cites background from "Analysis of Linear Iterative Learni..."
...[139], [141], [142], [161], [276], [317], [354]; frequency-domain analysis and/or synthesis based on...
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...[317] comprehensively explained the stability of HOILC scheme, norm-optimal ILC, predictive norm-optimal ILC, and adaptive ILC based on 2-D concepts....
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TL;DR: VRFT is a data-based method that permits to directly select the controller based on data, with no need for a model of the plant, based on a global model reference optimization procedure and does not require to access the plant for experiments many times so as to estimate the control cost gradient.
Abstract: This paper introduces the virtual reference feedback tuning (VRFT) approach for controller tuning in a nonlinear setup. VRFT is a data-based method that permits to directly select the controller based on data, with no need for a model of the plant. It is based on a global model reference optimization procedure and, therefore, does not require to access the plant for experiments many times so as to estimate the control cost gradient. For this reason, it represents a very appealing controller design methodology for many control applications.
255 citations
Additional excerpts
...The convergence analysis of this section has similarities with repetitive processes; see, e.g., [23], [ 24 ], and the recent interesting paper [25]....
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TL;DR: This paper supplies a presentation of experiments on a commercial robot that demonstrate the effectiveness of iterative learning control, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions.
Abstract: Iterative learning control (ILC) applies to control systems that perform the same finite-time tracking command repeatedly. It iteratively adjusts the command from one repetition to the next in order to reduce the tracking error. This creates a two-dimensional (2-D) system, with time step and repetition number as independent variables. The simplest form of ILC uses only one gain times one error in the previous repetition, and can be shown to converge to the zero-tracking error independent of the system dynamics. Hence, it appears very effective from a mathematical perspective. However, in practice, there are unacceptable learning transients. A zero-phase low-pass filter is introduced here to eliminate the worst transients. The main purpose of this paper is to supply a presentation of experiments on a commercial robot that demonstrate the effectiveness of this approach, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions. Experiments using a two-gain ILC reaches this error level in only three iterations. It is suggested that these two simple ILC laws are the equivalent for learning control of proportional and PD control in classical control system design. Thus, what was an impractical approach, becomes practical, easy to apply, and effective.
156 citations
TL;DR: In this article, a quadratic performance index is introduced as a method to establish a new iterative learning control law, which guarantees monotonic convergence of the error to zero if the original system is a discrete-time LTI system and satisfies a positivity condition.
Abstract: In this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law. With this new algorithm, monotonic convergence of the error to zero is guaranteed if the original system is a discrete-time LTI system and it satisfies a positivity condition. If the original system is not positive, two methods are derived to make the system positive. The effect of the choice of weighting parameters in the performance index on convergence rate is analysed. As a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm. A high-order version of the algorithm is also derived and its convergence analysed. The theoretical findings in this paper are highlighted with simulations.
121 citations
TL;DR: In this article, an iterative learning control (ILC) scheme is proposed to ensure trajectory-keeping in satellite formation flying, and robust ILC can be effectively utilized for satellite trajectory tracking, thus enabling time-variant formation flying between the leader and follower.
Abstract: This paper proposes an iterative learning control (ILC) scheme to ensure trajectory-keeping in satellite formation flying. Since satellites rotate the earth periodically, position-dependent disturbances can be considered time-periodic disturbances. This observation motivates the idea of repetitively compensating for external disturbances such as solar radiation, magnetic field, air drag, and gravity forces in an iterative, orbit-to-orbit manner. It is shown that robust ILC can be effectively utilized for satellite trajectory tracking, thus enabling time-variant formation flying between the leader- and follower-satellites. The validity of the results is illustrated through computational simulations. Copyright © 2009 John Wiley & Sons, Ltd.
114 citations
Cites background from "Analysis of Linear Iterative Learni..."
...Contract/grant sponsor: Institute of Medical System Engineering (iMSE) Contract/grant sponsor: Korea Science and Engineering Foundation; contract/grant number: 2009-0071105 and was then returned to its starting location before repeating the movement (see [3–5])....
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References
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Additional excerpts
...Note also that this last relationship is a form of Levenberg‐Marquardt [ 15 ] or modified Newton iteration which is familiar in finite-dimensional problems but, in this case, could equally well apply to an infinite dimensional problem....
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Book•
01 Jan 1966
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Abstract: "The monograph by T Kato is an excellent textbook in the theory of linear operators in Banach and Hilbert spaces It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory
In chapters 1, 3, 5 operators in finite-dimensional vector spaces, Banach spaces and Hilbert spaces are introduced Stability and perturbation theory are studied in finite-dimensional spaces (chapter 2) and in Banach spaces (chapter 4) Sesquilinear forms in Hilbert spaces are considered in detail (chapter 6), analytic and asymptotic perturbation theory is described (chapter 7 and 8) The fundamentals of semigroup theory are given in chapter 9 The supplementary notes appearing in the second edition of the book gave mainly additional information concerning scattering theory described in chapter 10
The first edition is now 30 years old The revised edition is 20 years old Nevertheless it is a standard textbook for the theory of linear operators It is user-friendly in the sense that any sought after definitions, theorems or proofs may be easily located In the last two decades much progress has been made in understanding some of the topics dealt with in the book, for instance in semigroup and scattering theory However the book has such a high didactical and scientific standard that I can recomment it for any mathematician or physicist interested in this field
Zentralblatt MATH, 836
19,846 citations
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Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.
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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.
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