Enhancing Iterative Learning Control With Fractional Power Update Law

Zihan Li; Dong Shen; Xinghuo Yu

doi:10.1109/JAS.2023.123525

Volume 10 Issue 5

May 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(5): 1137-1149

Z. H. Li, D. Shen, and X. H. Yu, “Enhancing iterative learning control with fractional power update law,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1137–1149, May 2023. doi: 10.1109/JAS.2023.123525

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Z. H. Li, D. Shen, and X. H. Yu, “Enhancing iterative learning control with fractional power update law,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1137–1149, May 2023. doi: 10.1109/JAS.2023.123525

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Enhancing Iterative Learning Control With Fractional Power Update Law

doi: 10.1109/JAS.2023.123525

Zihan Li^{1
,
,},
Dong Shen^{1
,
,},
Xinghuo Yu^{2
,
,
,}

1.
School of Mathematics, Renmin University of China, Beijing 100872, China
2.
School of Engineering, RMIT University, Melbourne VIC 3001, Australia

Funds: This work was supported by the National Natural Science Foundation of China (62173333) and Australian Research Council Discovery Program (DP200101199)

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Author Bio:
Zihan Li received the B.S. degree in mathematics from Hunan University in 2021. He is currently working toward the master degree with the School of Mathematics, Renmin University of China. His research interests include learning control and parameter estimation

Dong Shen (Senior Member, IEEE) received the B.S. and Ph.D. degrees in mathematics from Shandong University, and the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), in 2005 and 2010, respectively. From 2010 to 2012, he was a Post-Doctoral Fellow with the Institute of Automation, CAS. From 2012 to 2019, he was with the Beijing University of Chemical Technology. From 2016.02 to 2017.02, he was a Visiting Scholar at National University of Singapore, Singapore. From 2019.07 to 2019.08, he was a Visiting Research Fellow at RMIT University, Australia. Since 2020, he has been a Professor with the School of Mathematics, Renmin University of China. His research interests include iterative learning control, stochastic optimization, and distributed artificial intelligence. He is currently serving on the Editorial Board of International Journal of Robust and Nonlinear Control and IET Cyber-Systems and Robotics, and Early Career Advisory Board of IEEE/CAA Journal of Automatica Sinica

Xinghuo Yu (Fellow, IEEE) received B.Eng. and M.Eng. degrees in electrical and electronic engineering from the University of Science and Technology of China, in 1982 and 1984, and Ph.D. degree in control science and engineering from Southeast University, in 1988, respectively.He is a Distinguished Professor and a Vice-Chancellor’s Professorial Fellow at Royal Melbourne Institute of Technology (RMIT University), Australia. He was the President of IEEE Industrial Electronics Society in 2018 and 2019. His research interests include control systems, complex and intelligent systems, and future energy systems. He served as an Associate Editor of IEEE Transactions on Automatic Control, IEEE Transactions on Circuits and Systems I: Regular Papers, IEEE Transactions on Industrial Electronics and IEEE Transactions on Industrial Informatics. He received a number of awards and honors for his contributions, including 2013 Dr.-Ing. Eugene Mittelmann Achievement Award of IEEE Industrial Electronics Society, and 2018 M. A. Sargent Medal from Engineers Australia. He is an Honorary Fellow of Engineers Australia
Corresponding author: Xinghuo Yu, e-mail: xinghuo.yu@rmit.edu.au
Received Date: 2023-02-10
Revised Date: 2023-02-19
Accepted Date: 2023-02-23

Available Online: 2023-03-08

Abstract

Abstract

The P-type update law has been the mainstream technique used in iterative learning control (ILC) systems, which resembles linear feedback control with asymptotical convergence. In recent years, finite-time control strategies such as terminal sliding mode control have been shown to be effective in ramping up convergence speed by introducing fractional power with feedback. In this paper, we show that such mechanism can equally ramp up the learning speed in ILC systems. We first propose a fractional power update rule for ILC of single-input-single-output linear systems. A nonlinear error dynamics is constructed along the iteration axis to illustrate the evolutionary converging process. Using the nonlinear mapping approach, fast convergence towards the limit cycles of tracking errors inherently existing in ILC systems is proven. The limit cycles are shown to be tunable to determine the steady states. Numerical simulations are provided to verify the theoretical results.
- Asymptotic convergence,
- convergence rate,
- finite-iteration tracking,
- fractional power learning rule,
- limit cycles

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References(29)

References

[1]	D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control: A learning-based method for high performance tracking control,” IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96–114, 2006. doi: 10.1109/MCS.2006.1636313
[2]	D. Meng and J. Zhang, “Robust optimization-based iterative learning control for nonlinear systems with nonrepetitive uncertainties,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1001–1014, 2021. doi: 10.1109/JAS.2021.1003973
[3]	Y. Hui, R. Chi, B. Huang, and Z. Hou, “Extended state observer-based data-driven iterative learning control for permanent magnet linear motor with initial shifts and disturbances,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 3, pp. 1881–1891, 2021. doi: 10.1109/TSMC.2019.2907379
[4]	A. A. Armstrong, A. J. Wagoner Johnson, and A. G. Alleyne, “An improved approach to iterative learning control for uncertain systems,” IEEE Trans. Control Systems Technology, vol. 29, no. 2, pp. 546–555, 2021. doi: 10.1109/TCST.2019.2952327
[5]	D. Shen, “Practical learning-tracking framework under unknown nonrepetitive channel randomness,” IEEE Trans. Automatic Control, pp. 1–16, 2022.
[6]	A. Deutschmann-Olek, G. Stadler, and A. Kugi, “Stochastic iterative learning control for lumped- and distributed-parameter systems: A wiener-filtering approach,” IEEE Trans. Automatic Control, vol. 66, no. 8, pp. 3856–3862, 2021. doi: 10.1109/TAC.2020.3028839
[7]	Z. Wang, R. Zhou, C. Hu, and Y. Zhu, “Online iterative learning compensation method based on model prediction for trajectory tracking control systems,” IEEE Trans. Industrial Informatics, vol. 18, no. 1, pp. 415–425, 2022. doi: 10.1109/TII.2021.3085845
[8]	C. Hua, Y. Qiu, and X. Guan, “Event-triggered iterative learning containment control of model-free multiagent systems,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 51, no. 12, pp. 7719–7726, 2021. doi: 10.1109/TSMC.2020.2981404
[9]	F. H. Kong and I. R. Manchester, “Contraction analysis of nonlinear noncausal iterative learning control,” Systems &Control Letters, vol. 136, p. 104599, 2020.
[10]	Q. Yu and Z. Hou, “Adaptive fuzzy iterative learning control for high-speed trains with both randomly varying operation lengths and system constraints,” IEEE Trans. Fuzzy Systems, vol. 29, no. 8, pp. 2408–2418, 2021. doi: 10.1109/TFUZZ.2020.2999958
[11]	X. Bu and Z. Hou, “Adaptive iterative learning control for linear systems with binary-valued observations,” IEEE Trans. Neural Networks and Learning Systems, vol. 29, no. 1, pp. 232–237, 2018. doi: 10.1109/TNNLS.2016.2616885
[12]	X. Jin, “Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking,” Systems &Control Letters, vol. 89, pp. 16–23, 2016.
[13]	W. Xiong, L. Xu, T. Huang, X. Yu, and Y. Liu, “Finite-iteration tracking of singular coupled systems based on learning control with packet losses,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 50, no. 1, pp. 245–255, 2020. doi: 10.1109/TSMC.2017.2770160
[14]	W. Xiong, D. W. Ho, and S. Wen, “A periodic iterative learning scheme for finite-iteration tracking of discrete networks based on flexray communication protocol,” Information Sciences, vol. 548, pp. 344–356, 2021. doi: 10.1016/j.ins.2020.10.017
[15]	X. Cheng, H. Jiang, D. Shen, and X. Yu, “A novel adaptive gain strategy for stochastic learning control,” IEEE Trans. Cybernetics, pp. 1–12, 2022.
[16]	V. T. Haimo, “Finite time controllers,” SIAM Journal on Control and Optimization, vol. 24, no. 4, pp. 760–770, 1986. doi: 10.1137/0324047
[17]	S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000. doi: 10.1137/S0363012997321358
[18]	W. M. Haddad and A. L’Afflitto, “Finite-time stabilization and optimal feedback control,” IEEE Trans. Automatic Control, vol. 61, no. 4, pp. 1069–1074, 2016. doi: 10.1109/TAC.2015.2454891
[19]	S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, 2005. doi: 10.1016/j.automatica.2005.07.001
[20]	X. Yu, J.-X. Xu, Y. Hong, and S. Yu, “Analysis of a class of discrete-time systems with power rule,” Automatica, vol. 43, no. 3, pp. 562–566, 2007. doi: 10.1016/j.automatica.2006.09.013
[21]	H. Hou, X. Yu, L. Xu, K. Rsetam, and Z. Cao, “Finite-time continuous terminal sliding mode control of servo motor systems,” IEEE Trans. Industrial Electronics, vol. 67, no. 7, pp. 5647–5656, 2020. doi: 10.1109/TIE.2019.2931517
[22]	F. Wu, C. Li, and J. Lian, “Finite-time stability of switched nonlinear systems with state jumps: A dwell-time method,” IEEE Trans. Systems,Man,and Cybernetics: Systems, vol. 52, no. 10, pp. 6061–6072, 2022. doi: 10.1109/TSMC.2021.3134765
[23]	F. Tatari, H. Modares, C. Panayiotou, and M. Polycarpou, “Finite-time distributed identification for nonlinear interconnected systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 7, pp. 1188–1199, 2022. doi: 10.1109/JAS.2022.105683
[24]	Y. Liu, H. Li, R. Lu, Z. Zuo, and X. Li, “An overview of finite/fixed-time control and its application in engineering systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 12, pp. 2106–2120, 2022. doi: 10.1109/JAS.2022.105413
[25]	G. Sun, Z. Ma, and J. Yu, “Discrete-time fractional order terminal sliding mode tracking control for linear motor,” IEEE Trans. Industrial Electronics, vol. 65, no. 4, pp. 3386–3394, 2018. doi: 10.1109/TIE.2017.2748045
[26]	F. Li, Z. Wu, C. Yang, Y. Shi, T. Huang, and W. Gui, “A novel learning-based asynchronous sliding mode control for discrete-time semi-Markov jump systems,” Automatica, vol. 143, p. 110428, 2022. doi: 10.1016/j.automatica.2022.110428
[27]	S. Kuang, D. Dong, and I. R. Petersen, “Rapid Lyapunov control of finite-dimensional quantum systems,” Automatica, vol. 81, pp. 164–175, 2017. doi: 10.1016/j.automatica.2017.02.041
[28]	P. Ioannou and B. Fidan, Adaptive Control Tutorial. SIAM, 2006.
[29]	W. Zhou, M. Yu, and D. Huang, “A high-order internal model based iterative learning control scheme for discrete linear time-varying systems,” Int. Journal of Automation and Computing, vol. 12, no. 3, pp. 330–336, 2015. doi: 10.1007/s11633-015-0886-x

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Enhancing Iterative Learning Control With Fractional Power Update Law

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