Object
Title: Iterative learning control for over-determined, under-determined, and ill-conditioned systems
Contributor:
Gałkowski, Krzysztof - ed. ; Longman, Richard W. - ed. ; Rogers, Eric - ed.
Subtitle:
Multidimensional Systems nD and Iterative Learning Control
Group publication title:
Abstract:
This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. ; The Tikhonov regularization technique is discussed for computing the pseudoinverse to handle numerical instability. It is shown that for over-determined systems, the minimum error is never reached by a repetition invariant learning controller unless one knows the system exactly. ; For discrete time uniquely determined systems it is indicated that the inverse is usually ill-conditioned, and hence an approximate inverse based on a pseudoinverse is appropriate, treating the system as overdetermined. Using the structure of the system matrix, an enhanced Tikhonov regularization technique is developed which converges to zero tracking error. ; It is shown that the Tikhonov regularization is a form of linear quadratic ILC, and that the regularization approach solves the important practical problem of how to intelligently pick the weighting matrices in the quadratic cost. It is also shown how to use a modification of the Tikhonov-based quadratic cost in order to produce a frequency cutoff. This robustifies good learning transients, by reformulating the problem as an over-determined system.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
Pages:
Source:
AMCS, volume 13, number 1 (2003) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2003)
Last modified:
Oct 18, 2021
In our library since:
Oct 14, 2021
Number of object content hits:
84
All available object's versions:
https://zbc.uz.zgora.pl/publication/65885
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 24 (2014)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 23 (2013)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 22 (2012)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 21 (2011)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 20 (2010)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 19 (2009)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 18 (2008)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 17 (2007)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 16 (2006)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 15 (2005)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13, number 1 (2003)
- A functorial approach to the behaviour of multidimensional control systems
- Polynomial systems theory applied to the analysis and design of multidimensional systems
- Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
- An application of the Fourier transform to optimization of continuous 2-D systems
- Controllability and reconstructability of a system described by the N-D Roesser model
- Canonical forms of singular 1D and 2D linear systems
- Towards a framework for continuous and discrete multidimensional systems
- Linear repetitive process control theory applied to a physical example
- On the interaction between theory, experiments, and simulation in developing practical learning control algorithms
- Iterative learning control for over-determined, under-determined, and ill-conditioned systems
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13, number 2 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13, number 3 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13, number 4 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 13, number 1 (2003)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 12 (2002)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 11 (2001)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 10 (2000)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 9 (1999)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 8 (1998)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 7 (1997)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 6 (1996)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 5 (1995)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 4 (1994)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 3 (1993)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 2 (1992)
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International Journal of Applied Mathematics and Computer Science (AMCS),volume 1 (1991)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
| Edition name | Date |
|---|---|
| Iterative learning control for over-determined, under-determined, and ill-conditioned systems | Oct 18, 2021 |
