Abstract
In this paper, the problem of iterative learning control is considered for a class of one-sided Lipschitz nonlinear systems. For such nonlinear systems, open-loop and closed-loop P-type learning algorithms with initial state learning are adopted, respectively. Furthermore, the convergence conditions of the P-type learning algorithms are established. It is shown that both algorithms can guarantee the system output converges to the desired one on the whole time interval. A numerical example is constructed to illustrate the effectiveness of the proposed learning algorithms.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Z. Bien and J. X. Xu, Iterative Learning Control: Analysis, Design, Integration and Applications, Kluwer Academic Publishers, Boston, 1998.
J. X. Xu and Y. Tan, Linear and Nonlinear Iterative Learning Control, Springer-Verlag, Berlin, 2003.
M. Sun and D. Wang, “Initial shift issues on discretetime iterative learning control with system relative degree,” IEEE Transactions on Automatic Control, vol. 48, no. 1, pp. 144–148, January 2003.
K. L. Moore, Y. Chen, and V. Bahl, “Monotonically convergent iterative learning control for linear discrete-time systems,” Automatica, vol. 41, no. 9, pp. 1529–1537, September 2005.
Z. Hou, J. X. Xu, and H. Zhong, “Freeway traffic control using iterative learning control-based ramp metering and speed signaling,” IEEE Transactions on vehicular technology, vol. 56, no. 2, pp. 466–477, March 2007.
X. Ruan, Z. Bien, and Q. Wang, “Convergence properties of iterative learning control processes in the sense of the Lebesgue-p norm,” Asian Journal of Control, vol. 14, no. 4, pp. 1095–1107, July 2012.
Q. Fu, P. Gu, and J. Wu, “ Decentralized iterative learning control for large-scale interconnected linear systems with fixed initial shifts,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 1991–2000, October 2017.
W. He, T. Meng, X. He, and S. S. Ge, “ Unified iterative learning control for flexible structures with input constraints,” Automatica, vol. 96, no. 10, pp. 326–336, October 2018.
D. Meng and K. L. Moore, “ Robust iterative learning control for nonrepetitive uncertain systems,” IEEE Transactions on Automatic Control, vol. 62, no. 2, pp. 907–913, February 2017.
A. Isidori, Nonlinear Control Systems, Springer-Verlag, New York, 1989.
X. Xie, D. Yue, and S. Hu, “ Fault estimation observer design of discrete-time nonlinear systems via a joint real-time scheduling law,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 7, pp. 1451–1463, July 2017.
X. Xie, D. Yue, J. H. Park, and H. Li, “ Relaxed fuzzy observer design of discrete-time nonlinear systems via two effective technical measures,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 5, pp. 2833–2845, October 2018.
Y. Yang, C. Xu, D. Yue, and X. Xie, “Output feedback tracking control of a class of continuous-time nonlinear systems via adaptive dynamic programming approach,” Information Sciences, vol. 469, pp. 1–13, December 2018.
H. S. Ahn, C. H. Choi, and K. B. Kim, “ Iterative learning control for a class of nonlinear systems,” Automatica, vol. 29, no. 6, pp. 1575–1578, Novermber 1993.
Y. Q. Chen, C. Wen, Z. Gong, and M. Sun, “An iterative learning controller with initial state learning,” IEEE Transactions on Automatic Control, vol. 44, no. 2, pp. 371–376, Feburary 1999.
M. Sun, D. Wang, and Y. Wang, “Sampled-data iterative learning control with well-defined relative degree,” International Journal of Robust and Nonlinear Control, vol. 14, no. 8, pp. 719–739, May 2004.
X. Bu, F. Yu, Z. Hou, and F. Wang, “Iterative learning control for a class of nonlinear systems with random packet losses,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 567–580, February 2013.
S. Liu, J. Wang, and W. Wei, “A study on iterative learning control for impulsive differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 24, no. 1, pp. 4–10, July 2015.
L. Wang, X. Li, and D. Shen, “Sampled-data iterative learning control for continuous-time nonlinear systems with iteration-varying lengths,” International Journal of Robust and Nonlinear Control, vol. 28, no. 8, pp. 3073–3091, May 2018.
M. Yu, W. Zhou, and B. Liu, “On iterative learning control for MIMO nonlinear systems in the presence of timeiteration-varying parameters,” Nonlinear Dynamics, vol. 89, no. 4, pp. 2561–2571, September 2017.
L. Feng, Y. Chai, S. Xu, and Z. Yang, “ Observer-based fault estimators using iterative learning scheme for nonlinear time-delay systems with intermittent faults,” International Journal of Robust and Nonlinear Control, vol. 27, no. 17, pp. 3412–3432, November 2017.
G. Hu, “Observers for one-sided Lipschitz non-linear systems,” IMA Journal of Mathematical Control and Information, vol. 23, no. 4, pp. 395–401, December 2006.
M. Xu, G. Hu, and Y. Zhao, “Reduced-order observer for one-sided Lipschitz nonlinear systems” IMA Journal of Mathematical Control and Information, vol. 26, no. 3, pp. 299–317, August 2009.
Y. Zhao, J. Tao, and N. Z. Shi, “A note on observer design for one-sided Lipschitz nonlinear systems,” Systems & Control Letters, vol. 59, no. 1, pp. 66–71, January 2010.
M. Abbaszadeh and H. J. Marquez, “Nonlinear observer design for one-sided Lipschitz systems,” Proceeding of the American Control Conference, Baltimore, USA, pp. 5284–5289, June 2010.
S. Raghavan and J. K. Hedrick, “Observer design for a class of nonlinear systems,” International Journal of Control, vol. 59, no. 2, pp. 515–528, February 1994.
W. Yu, P. DeLellis, G. Chen, M. D. Bernardo, and J. Kurths, “Distributed adaptive control of synchronization in complex networks,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2153–2158, August 2012.
M. Hussain, M. Rehan, C. K. Ahn, and M. Tufail, “Robust anti-windup for one-sided Lipschitz systems subject to input saturation and applications,” IEEE Transactions on Industrial Electronics, vol. 65, no. 12, pp. 9706–9716, March 2018.
W. Zhang, H. Su, H. Wang, and Z. Han, “Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4968–4977, December 2012.
X. Cai, H. Gao, L. Liu, W. Zhang, “Control design for one-sided Lipschitz nonlinear differential inclusions,” ISA Transactions, vol. 53, no. 2, pp. 298–304, March 2014.
J. Song and S. He, “Robust finite-time H∞ control for onesided Lipschitz nonlinear systems via state feedback and output feedback,” Journal of The Franklin Institute, vol. 352, no. 8, pp. 3250–3266, August 2015.
W. Zhang, H. Su, F. Zhu, and G. Azar, “Unknown input observer design for one-sided Lipschitz nonlinear systems,” Nonlinear Dynamics, vol. 79, no. 2, pp. 1469–1479, January 2015.
N. C. Nguyen and H. Trinh, “Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay,” Applied Mathematics and Computation, vol. 286, no. 8, pp. 57–71, August 2016.
W. Zhang, H. Su, F. Zhu, and S. P. Bhattacharyya, “Improved exponential observer design for one-sided Lipschitz nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 26, no. 18, pp. 3958–3973, December 2016.
Y. Dong, W. Liu, and S. Liang, “ Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties,” International Journal of Robust and Nonlinear Control, vol. 27, no. 11, pp. 1974–1998, July 2017.
M. Sun and D. Wang, “Sampled-data iterative learning control for nonlinear systems with arbitrary relative degree,” Automatica, vol. 37, no. 2, pp. 283–289, Feburary 2001.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Xiangpeng Xie under the direction of Editor Jessie (Ju H.) Park. This work was supported in part by the National Natural Science Foundation of China under Grants 61374104 and 61773170, in part by the Natural Science Foundation of Guangdong Province under Grant 2016A030313505, and in part by the Scholarship from China Scholarship Council under Grant 201806150118.
Panpan Gu received his B.S. degree from Chaohu University, Hefei, China, in 2013. He received his M.S. degree from Suzhou University of Science and Technology, Suzhou, China, in 2016. He is currently pursuing his Ph.D. degree at the School of Automation Science and Engineering, South China University of Technology. He is currently an exchange Ph.D. student in the School of Engineering, University of California, Merced. His research interest is iterative learning control.
Senping Tian received his B.S. and M.S. degrees from Central China Normal University, Wuhan, China, in 1982 and 1988, respectively, and the Ph.D. degree from South China University of Technology, Guangzhou, China, in 1999. He has been a professor with School of Automation Science and Engineering, South China University of Technology, since 2008. His research interests include theory and algorithms on iterative learning control for nonlinear systems, optimization and control of large-scale systems, the stability and the qualitative theory of differential equations.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gu, P., Tian, S. P-type Iterative Learning Control with Initial State Learning for One-sided Lipschitz Nonlinear Systems. Int. J. Control Autom. Syst. 17, 2203–2210 (2019). https://doi.org/10.1007/s12555-018-0891-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-018-0891-2