Abstract
This paper analyses the concept of a Limit Set in Parameter Optimal Iterative Learning Control (ILC). We investigate the existence of stable and unstable parts of Limit Set and demonstrates that they will often exist in practice. This is illustrated via a 2-dimensional example where the convergence of the learning algorithm is analyzed from the error’s dynamic behaviour. These ideas are extended to the N-dimensional cases by analogy and example.
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S. Arimoto, S. Kawamura, F. Miyazaki. Bettering Operations and Robot Learning. Journal of Robotic Systems, vol. 1, no. 1, pp. 123–140, 1984.
K. Moore. Iterative Learning Control for Deterministic Systems. Springer, London, 1993.
K. Moore, J-X. Xu. Editorial: Special Issue on Iterative Learning Control. Interational Journal of Control, vol. 73, no. 10, pp. 819–823, 2000.
J. J. Hatönen, D. H. Owens, K. Feng. Basis Functions and Parameter Optimization in High-Order Iterative Learning Control. Automatica, vol. 42, no. 2, pp. 287–294, 2006.
D. H. Owens, J. J. Hatönen. Iterative Learning Control — an Optimization Paradigm. Annual Reviews in Control, vol 29, no. 1, pp. 57–70, 2005.
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David H. Owens obtained his B.Sc. degree in Theoretical Physics in 1969 from Imperial College London and a Ph.D. degree in Nuclear reactor Dynamics and Control whilst working at the UK Atomic energy Authority in 1973. He has held academic positions at the Universities of Sheffield, Strathclyde and Exeter. He is currently the Head of the Department of Automatic Control and Systems Engineering and Dean of the Faculty of Engineering at The University of Sheffield.
He is the author of over 460 refereed technical publications and the author or co-author of four texts on multivariable, multipass and repetitive control systems. His research interests span a wide range of theoretical and applied topics including robust and adaptive control and algorithms for iterative and repetitive control.
Maria Tomas-Rodriguez obtained her B.Sc. degree in physics in 1999 from Complutense University of Madrid, Spain. She obtained her M.Sc degree in control systems engineering in 2001, and her Ph.D. in nonlinear control systems in 2005 from The Sheffield University. During 2003 and 2004 she worked as Research Assistant at the Automatic Control and Systems Engineering Department at The University of Sheffield. She is currently working as postdoctoral Research Assistant at the E&E. Engineering Department, Imperial College.
Her research interests include nonlinear systems stability, ILC, feedback control systems, optimal control, dynamical systems modelling. She is currently working at helicopter stability and control.
Jari Hatönen was born in 1971 in Finland. He received his M.Sc degree in electrical engineering in 2000 from Helsinki University of Technology, Finland, and his Ph.D. degree in automation and information technology in 2004 from University of Oulu, Finland. He is currently working as a researcher for Borealis A/S in the Process Research Group.
His research interests include iterative learning control, repetitive control, active control of vibration, image analysis based control of mineral flotation, and mathematical modeling of polymerisation.
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Owens, D.H., Tomas-Rodriguez, M. & Hatönen, J.J. Limiting behaviour in Parameter Optimal Iterative Learning Control. Int J Automat Comput 3, 222–228 (2006). https://doi.org/10.1007/s11633-006-0222-6
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DOI: https://doi.org/10.1007/s11633-006-0222-6