Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking

David H. Owens; Chris T. Freeman; Bing Chu

doi:10.1007/s11633-015-0888-8

June 2015

Article Contents

David H. Owens, Chris T. Freeman and Bing Chu. Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking. International Journal of Automation and Computing, vol. 12, no. 3, pp. 243-253, 2015. doi: 10.1007/s11633-015-0888-8

Cite as: David H. Owens, Chris T. Freeman and Bing Chu. Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking. International Journal of Automation and Computing, vol. 12, no. 3, pp. 243-253, 2015. doi: 10.1007/s11633-015-0888-8

Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S3JD, UK;
School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK;
Advanced Robotics Division, Italian Institute of Technology, Genoa, Italy

Received: 2014-03-26

Abstract

Norm optimal iterative learning control (NOILC) has recently been applied to iterative learning control (ILC) problems in which tracking is only required at a subset of isolated time points along the trial duration. This problem addresses the practical needs of many applications, including industrial automation, crane control, satellite positioning and motion control within a medical stroke rehabilitation context. This paper provides a substantial generalization of this framework by providing a solution to the problem of convergence at intermediate points with simultaneous tracking of subsets of outputs to reference trajectories on subintervals. This formulation enables the NOILC paradigm to tackle tasks which mix "point to point" movements with linear tracking requirements and hence substantially broadens the application domain to include automation tasks which include welding or cutting movements, or human motion control where the movement is restricted by the task to straight line and/or planar segments. A solution to the problem is presented in the framework of NOILC and inherits NOILC'swell-defined convergence properties. Design guidelines and supporting experimental results are included.
- Iterative learning control,
- learning control,
- optimization,
- linear systems,
- robotics

References

[1]	S. Arimoto, F. Miyazaki, S. Kawamura. Bettering operation of robots by learning. Journal of Robotic Systems, vol.1, no. 2, pp. 123-140, 1984.
[2]	D. A. Bristow, M. Tharayil, A. G. Alleyne. A survey of iterative learning control: A learning-based method for highperformance tracking control. IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96-114, 2006.
[3]	H. S. Ahn, Y. Chen, K. L. Moore. Iterative learning control: Brief survey and categorization. IEEE Transactions on Systems, Man, and Cybernetics, Part C, vol. 37, no. 6, 1099-1121, 2007.
[4]	D. H. Owens, C. T. Freeman, B. Chu. Multivariable norm optimal iterative learning control with auxiliary optimization. International Journal of Control, vol. 86, no. 6, pp. 1026-1045, 2013.
[5]	D. H. Owens, C. T. Freeman, T. Van Dinh. Norm optimal iterative learning control with intermediate point weighting: Theory, algorithms, and experimental evaluation. IEEE Transactions on Control Systems Technology, vol. 21, no. 3, pp. 999-1007, 2013.
[6]	G. Pipeleers, J. Swevers. A data-driven constrained normoptimal iterative learning control framework for LTI systems. IEEE Transactions on Control Systems Technology, vol. 21, no. 2, pp. 546-551, 2013.
[7]	T. D. Son, H. S. Ahn, K. L. Moore. Iterative learning control in optimal tracking problems with specified data points. Automatica, vol. 49, no. 5, pp. 1465-1472, 2013.
[8]	S. H. Zhou, Y. Tan, D. Oetomo, C. T. Freeman, E. Burdet, I. Mareels. Point-to-point learning in human motor systems. In Proceedings of the American Control Conference, IEEE, Washington, USA, pp. 5923-5928, 2013.
[9]	C. T. Freeman, T. Exell, K. L. Meadmore, E. Hallewell, A. M. Hughes. Computational models of upper-limb motion during functional reaching tasks for application in FESbased stroke rehabilitation. Biomedical Engineering, to be published.
[10]	K. L. Moore, M. Ghosh, Y. Q. Chen. Spatial-based iterative learning control for motion control applications. Meccanica, vol. 42, no. 2, pp. 167-175, 2007.
[11]	S. K. Sahoo, S. K. Panda, J. X. Xu. Application of spatial iterative learning control for direct torque control of switched reluctance motor drive. In Proceedings of IEEE Power Engineering Society General Meeting, IEEE, Tampa, USA, pp. 1-7, 2007.
[12]	Y. H. Yang, C. L. Chen. Spatial-based adaptive iterative learning control of nonlinear rotary systems with spatially periodic parametric variation. International Journal of Innovative Computing, Information and Control, vol. 7, no. 6, pp. 3407-3417, 2011.
[13]	K. Furuta, M. Yamakita. The design of a learning control system for multivariable systems. In Proceedings of IEEE International Symposium on Intelligent Control, IEEE, Philadelphia, USA, pp. 371-376, 1987.
[14]	K. Kinosita, T. Sogo, N. Adachi. Iterative learning control using adjoint systems and stable inversion. Asian Journal of Control, vol. 4, no. 1, pp. 60-67, 2002.
[15]	D. H. Owens, J. J. Hatonen, S. Daley. Robust monotone gradient-based discrete-time iterative learning control. International Journal of Robust and Nonlinear Control, vol. 19, no. 6, pp. 634-661, 2009.
[16]	N. Amann, D. H. Owens, E. Rogers. Iterative learning control using optimal feedback and feed-forward actions. International Journal of Control, vol. 65, no. 2, pp. 277-293, 1996.
[17]	S. Gunnarsson, M. Norrlöf. On the design of ILC algorithms using optimization. Automatica, vol. 37, no. 12, pp. 2011-2016, 2001.
[18]	J. H. Lee, K. S. Lee, W. C. Kim. Model-based iterative learning control with a quadratic criterion for timevarying linear systems. Automatica, vol. 36, no. 5, pp. 641-657, 2000.
[19]	K. L. Barton, A. G. Alleyne. A norm optimal approach to time-varying ILC with application to a multi-axis robotic testbed. IEEE Transactions on Control Systems Technology, vol. 19, no. 1, pp. 166-180, 2011.
[20]	E. Rogers, D. H. Owens, H. Werner, C. T. Freeman, P. L. Lewin, S. Kichhoff, C. Schmidt, G. Lichtenberg. Norm optimal iterative learning control with application to problems in accelerator based free electron lasers and rehabilitation robotics. European Journal of Control, vol. 16, no. 5, pp. 497-524, 2010.
[21]	N. Amann, D. H. Owens, E. Rogers. Iterative learning control for discrete-time systems with exponential rate of convergence. IEE Proceedings of Control Theory and Applications, vol. 143, no. 2, 217-224, 1996.
[22]	N. Amann, D. H. Owens, E. Rogers. Predictive optimal iterative learning control. International Journal of Control, vol. 69, no. 2, pp. 203-226, 1998.
[23]	B. Chu, D. H. Owens. Accelerated norm-optimal iterative learning control algorithms using successive projection. International Journal of Control, vol. 82, no. 8, pp. 1469-1484, 2009.
[24]	B. Chu, D. H. Owens. Iterative learning control for constrained linear systems. International Journal of Control, vol. 83, no. 7, pp. 1397-1413, 2010.
[25]	D. H. Owens, B. Chu, E. Rogers, C. T. Freeman, and P. L. Lewin. Influence of nonminimum phase zeros on the performance of optimal continuous-time iterative learning control. IEEE Transactions on Control Systems Technology, vol. 22, no. 3, pp. 1151-1158, 2014.
[26]	D. H. Owens, B. Chu. Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control. International Journal of Control, vol. 83, no. 10, pp. 2012-2027, 2010.

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Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S3JD, UK;

School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK;

Advanced Robotics Division, Italian Institute of Technology, Genoa, Italy

Received: 2014-03-26

Key words:

Abstract: Norm optimal iterative learning control (NOILC) has recently been applied to iterative learning control (ILC) problems in which tracking is only required at a subset of isolated time points along the trial duration. This problem addresses the practical needs of many applications, including industrial automation, crane control, satellite positioning and motion control within a medical stroke rehabilitation context. This paper provides a substantial generalization of this framework by providing a solution to the problem of convergence at intermediate points with simultaneous tracking of subsets of outputs to reference trajectories on subintervals. This formulation enables the NOILC paradigm to tackle tasks which mix "point to point" movements with linear tracking requirements and hence substantially broadens the application domain to include automation tasks which include welding or cutting movements, or human motion control where the movement is restricted by the task to straight line and/or planar segments. A solution to the problem is presented in the framework of NOILC and inherits NOILC'swell-defined convergence properties. Design guidelines and supporting experimental results are included.

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Reference (26)

[1]	S. Arimoto, F. Miyazaki, S. Kawamura. Bettering operation of robots by learning. Journal of Robotic Systems, vol.1, no. 2, pp. 123-140, 1984.
[2]	D. A. Bristow, M. Tharayil, A. G. Alleyne. A survey of iterative learning control: A learning-based method for highperformance tracking control. IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96-114, 2006.
[3]	H. S. Ahn, Y. Chen, K. L. Moore. Iterative learning control: Brief survey and categorization. IEEE Transactions on Systems, Man, and Cybernetics, Part C, vol. 37, no. 6, 1099-1121, 2007.
[4]	D. H. Owens, C. T. Freeman, B. Chu. Multivariable norm optimal iterative learning control with auxiliary optimization. International Journal of Control, vol. 86, no. 6, pp. 1026-1045, 2013.
[5]	D. H. Owens, C. T. Freeman, T. Van Dinh. Norm optimal iterative learning control with intermediate point weighting: Theory, algorithms, and experimental evaluation. IEEE Transactions on Control Systems Technology, vol. 21, no. 3, pp. 999-1007, 2013.
[6]	G. Pipeleers, J. Swevers. A data-driven constrained normoptimal iterative learning control framework for LTI systems. IEEE Transactions on Control Systems Technology, vol. 21, no. 2, pp. 546-551, 2013.
[7]	T. D. Son, H. S. Ahn, K. L. Moore. Iterative learning control in optimal tracking problems with specified data points. Automatica, vol. 49, no. 5, pp. 1465-1472, 2013.
[8]	S. H. Zhou, Y. Tan, D. Oetomo, C. T. Freeman, E. Burdet, I. Mareels. Point-to-point learning in human motor systems. In Proceedings of the American Control Conference, IEEE, Washington, USA, pp. 5923-5928, 2013.
[9]	C. T. Freeman, T. Exell, K. L. Meadmore, E. Hallewell, A. M. Hughes. Computational models of upper-limb motion during functional reaching tasks for application in FESbased stroke rehabilitation. Biomedical Engineering, to be published.
[10]	K. L. Moore, M. Ghosh, Y. Q. Chen. Spatial-based iterative learning control for motion control applications. Meccanica, vol. 42, no. 2, pp. 167-175, 2007.
[11]	S. K. Sahoo, S. K. Panda, J. X. Xu. Application of spatial iterative learning control for direct torque control of switched reluctance motor drive. In Proceedings of IEEE Power Engineering Society General Meeting, IEEE, Tampa, USA, pp. 1-7, 2007.
[12]	Y. H. Yang, C. L. Chen. Spatial-based adaptive iterative learning control of nonlinear rotary systems with spatially periodic parametric variation. International Journal of Innovative Computing, Information and Control, vol. 7, no. 6, pp. 3407-3417, 2011.
[13]	K. Furuta, M. Yamakita. The design of a learning control system for multivariable systems. In Proceedings of IEEE International Symposium on Intelligent Control, IEEE, Philadelphia, USA, pp. 371-376, 1987.
[14]	K. Kinosita, T. Sogo, N. Adachi. Iterative learning control using adjoint systems and stable inversion. Asian Journal of Control, vol. 4, no. 1, pp. 60-67, 2002.
[15]	D. H. Owens, J. J. Hatonen, S. Daley. Robust monotone gradient-based discrete-time iterative learning control. International Journal of Robust and Nonlinear Control, vol. 19, no. 6, pp. 634-661, 2009.
[16]	N. Amann, D. H. Owens, E. Rogers. Iterative learning control using optimal feedback and feed-forward actions. International Journal of Control, vol. 65, no. 2, pp. 277-293, 1996.
[17]	S. Gunnarsson, M. Norrlöf. On the design of ILC algorithms using optimization. Automatica, vol. 37, no. 12, pp. 2011-2016, 2001.
[18]	J. H. Lee, K. S. Lee, W. C. Kim. Model-based iterative learning control with a quadratic criterion for timevarying linear systems. Automatica, vol. 36, no. 5, pp. 641-657, 2000.
[19]	K. L. Barton, A. G. Alleyne. A norm optimal approach to time-varying ILC with application to a multi-axis robotic testbed. IEEE Transactions on Control Systems Technology, vol. 19, no. 1, pp. 166-180, 2011.
[20]	E. Rogers, D. H. Owens, H. Werner, C. T. Freeman, P. L. Lewin, S. Kichhoff, C. Schmidt, G. Lichtenberg. Norm optimal iterative learning control with application to problems in accelerator based free electron lasers and rehabilitation robotics. European Journal of Control, vol. 16, no. 5, pp. 497-524, 2010.
[21]	N. Amann, D. H. Owens, E. Rogers. Iterative learning control for discrete-time systems with exponential rate of convergence. IEE Proceedings of Control Theory and Applications, vol. 143, no. 2, 217-224, 1996.
[22]	N. Amann, D. H. Owens, E. Rogers. Predictive optimal iterative learning control. International Journal of Control, vol. 69, no. 2, pp. 203-226, 1998.
[23]	B. Chu, D. H. Owens. Accelerated norm-optimal iterative learning control algorithms using successive projection. International Journal of Control, vol. 82, no. 8, pp. 1469-1484, 2009.
[24]	B. Chu, D. H. Owens. Iterative learning control for constrained linear systems. International Journal of Control, vol. 83, no. 7, pp. 1397-1413, 2010.
[25]	D. H. Owens, B. Chu, E. Rogers, C. T. Freeman, and P. L. Lewin. Influence of nonminimum phase zeros on the performance of optimal continuous-time iterative learning control. IEEE Transactions on Control Systems Technology, vol. 22, no. 3, pp. 1151-1158, 2014.
[26]	D. H. Owens, B. Chu. Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control. International Journal of Control, vol. 83, no. 10, pp. 2012-2027, 2010.

Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking

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通讯作者: 陈斌, bchen63@163.com

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Generalized Norm Optimal Iterative Learning Control with Intermediate Point and Sub-interval Tracking

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S3JD, UK; School of Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, UK; Advanced Robotics Division, Italian Institute of Technology, Genoa, Italy

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