Parameter optimization in iterative learning control

Owens, D.H.; Feng, Kai

doi:10.1080/0020717031000121410

Cited by 106 publications

(71 citation statements)

References 11 publications

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“…In addition, the feedback term requires a full knowledge of the state of the system, which either requires instrumentation that can measure the states (possibly resulting in an expensive measurement set-up) or the inclusion of a state-observer into the NOILC algorithm. Therefore, it is an important question whether or not there exist structurally (in terms of implementation and instrumentation) simpler algorithms that would still result at least in monotonic convergence, as is discussed in (Owens and Feng, 2003). A natural starting point for answering this question is the Arimototype ILC algorithm…”

Section: Parameter-optimal Ilcmentioning

confidence: 99%

Iterative Learning Control — Monotonicity and Optimization

Owens¹,

Daley²

2008

International Journal of Applied Mathematics and Computer Science

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The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.

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Section: Parameter-optimal Ilcmentioning

confidence: 99%

Iterative Learning Control — Monotonicity and Optimization

Owens¹,

Daley²

2008

International Journal of Applied Mathematics and Computer Science

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“…Within this framework the plant and controller are written as matrices and the problems is transferred from a 2D (time and iteration) problem into a 1D (iteration) problem. (Phan et al, 2000;Hätönen, 2004;Norrlöf and Gunnarsson, 2002;Norrlöf, 2000b;Harte et al, 2005;Hakvoort et al, 2008;Moore, 2001;Owens and Feng, 2003. ) Define a discrete time plant obeying 16) with u(t) ∈ R r 1 , y(t) ∈ R r 2 , x(t) ∈ R m and A, B, C and D of appropriate dimensions.…”

Section: Lifted System Representationmentioning

confidence: 99%

Robust stability for iterative learning control

Bradley

French

2009

2009 American Control Conference

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This thesis examines the notion of the long term robust stability of iterative learning control (ILC) systems engaged in trajectory tracking, using a robust stability theorem based on a biased version of the nonlinear gap metric. This is achieved through two main results:The first concerns the establishment of a nonlinear robust stability theorem, where signals are measured relative to a given trajectory. Although primarily motivated by ILC, the theorem provided is applicable to a wider range of problems. This is due to its development being made independently of any particular signal space, provided the space is furnished with a definition of causality. The theorem's formulation therefore permits its implementation on single-or multi-dimensional problems in a variety of different settings. Necessitated by an ILC constraint concerning reference signals, the trajectory that stability is measured relative to must often lie outside the signal space that is chosen. The robust stability theorem is therefore devised to address signals that lie in extended signal spaces throughout. Additionally, the theorem is applicable to nonlinear systems, and it is shown that the biased gap measure collapses to the standard nonlinear gap measure when the bias is set to zero. It is also shown to collapse to the classical linear gap when restricting the analysis to certain linear systems.The second result applies the robust stability theorem to ILC using a 2D signal space.Initially the subject of ILC is reviewed and some of the problems associated with controllers are described; in particular the issues of long-term stability and the criteria for convergence. ILC algorithms expressed in the 'lifted system' or 'supervector' formulation are discussed and then analysed using the biased robust stability theorem. Results are presented regarding the use of filtering in ILC algorithms to aid robustness, and also the robustness of inverse model-based techniques. The robust stability tool applied to ILC in this thesis is not restricted in its analysis to algorithms which are 'causal' (in an ILC sense); and is based on a general unstructured uncertainty model in contrast to the existing literature, whereby uncertainties are typically constrained to additive, multiplicative or parametric models.

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“…The concepts of Parameter Optimal Iterative Learning Control (POILC) was introduced by Owens and Feng [4] and now has several different realisations (see [6] for a recent review). The basic idea is, given a plant description y = Gu + d and the control law u k+1 = u k + β k+1 Ke k choose the free Figure 1: Log||e k || for a generic system "learning gain" β k+1 to minimize the performance index…”

Section: Limit Sets and Basic Poilc Propertiesmentioning

confidence: 99%

“…This first part of this paper is concerned with the analysis of the limiting behaviour of ParameterOptimal Iterative Learning Control POILC introduced in Owens and Feng [4] and its generalization [5]. This extends the results in [7] and forms a motivation for the second part.…”

Section: Introductionmentioning

confidence: 99%

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Limit sets and switching strategies in parameter-optimal iterative learning control

Owens

Tomás-Rodrı́guez

Daley

2008

International Journal of Control

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This paper characterizes the existence and form of the possible limit error signals in typical parameter-optimal Iterative Learning Control. The set of limit errors has attracting and repelling components and the behaviour of the algorithm in the vicinity of these sets can be associated with the undesirable properties of apparent (but in fact temporary) convergence or permanent slow convergence properties in practice. The avoidance of these behaviours in practice is investigated using novel switching strategies. Deterministic strategies are analysed to prove the feasibility of the concept by proving that each of a number of such strategies is guaranteed to produce global convergence of errors to zero independent of the details of plant dynamics. For practical applications a random switching strategy is proposed to replace these approaches and shown, by example, to produce substantial potential improvements when compared with the non-switching case. The work described in this paper is covered by pending patent applications in the UK and elsewhere.

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Parameter optimization in iterative learning control

Cited by 106 publications

References 11 publications

Iterative Learning Control — Monotonicity and Optimization

Iterative Learning Control — Monotonicity and Optimization

Robust stability for iterative learning control

Limit sets and switching strategies in parameter-optimal iterative learning control

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