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Robust adaptive iterative learning control for nonrepetitive systems with iteration-varying parameters and initial state

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Abstract

This paper explores how to construct an adaptive iteration learning control (AILC) mechanism for a class of discrete-time nonrepetitive systems subject to iteration-varying unknown parameters and unidentical initial condition. Firstly, for the linear discrete-time nonrepetitive systems, by minimizing the discrepancy of the real system outputs from the estimated system outputs, a gradient-type adaptation law is designed to estimate the system lower triangular parameter matrix and the system initial state. Especially, the current parametric estimation is updated by virtue of the input-output data and the previous estimation. Secondly, an AILC mechanism is constructed based on the estimated system lower triangular parameter matrix, where the control input algorithm and the adaptation law are scheduled in an interactive mode. Thirdly, the boundedness of the estimation error between the real system matrix and the estimation one is derived by means of vector norm theory. Based on the boundedness of the estimation error, the robust condition of the proposed AILC is given. Finally, the proposed AILC is investigated for a class of nonlinear affine systems and the corresponding results are captured. Simulation results illustrate the validity and effectiveness of the proposed AILC schemes.

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References

  1. Xiao SY, Dong JX (2021) Cooperative fault-tolerant fuzzy tracking control for nonlinear multiagent systems under directed network topology via a hierarchical control scheme. Int J Robust Nonlinear Control 31(3):832–854

    Article  MathSciNet  Google Scholar 

  2. Li TR, Wang WQ, Chen WM (2021) Event-triggered observer-based H\(_{\infty }\) control of switched linear systems with time-varying delay. Int J Syst Sci. https://doi.org/10.1080/00207721.2020.1868610

    Article  MathSciNet  Google Scholar 

  3. Zhang XM, Han QL, Zhang BL (2017) An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems. IEEE Trans Ind Inform 13:4–16

    Article  Google Scholar 

  4. Bristow DA, Tharayil M, Alleyne AG (2006) A survey of iterative learning control: a learning-based method for high-performance tracking control. IEEE Control Syst Mag 26(3):96–114

    Article  Google Scholar 

  5. Ahn HS, Chen YQ, Moore KL (2007) Iterative learning control: brief survey and categorization. IEEE Trans Hum Mach Syst 37(6):1099–1121

    Google Scholar 

  6. Shen D, Wang YQ (2014) Survey on stochastic iterative learning control. J Process Control 24(12):64–77

    Article  Google Scholar 

  7. Arimoto S, Kawamura S, Miyazaki F (1984) Bettering operation of robots by learning. J Robot Syst 1(2):123–140

    Article  Google Scholar 

  8. Tayebi A (2004) Adaptive iterative learning control for robot manipulators. Automatica 40(7):1195–1203

    Article  MathSciNet  Google Scholar 

  9. Xu JX, Hu QP, Lee TH, Yamamoto S (2001) Iterative learning control with Smith time delay compensator for batch processes. J Process Control 11(3):321–328

    Article  Google Scholar 

  10. Shen D (2018) Data-driven learning control for stochastic nonlinear systems: multiple communication constraints and limited storage. IEEE Trans Neural Netw Learn Syst 29(6):2429–2440

    Article  MathSciNet  Google Scholar 

  11. Liu J, Zhang YM, Ruan X (2019) Iterative learning control for a class of uncertain nonlinear systems with current state feedback. Int J Syst Sci 50(10):1889–1901

    Article  MathSciNet  Google Scholar 

  12. Hu M, Du HJ, Ling SF, Zhou ZY, Li Y (2004) Motion control of an electrostrictive actuator. Mechatronics 14(2):153–161

    Article  Google Scholar 

  13. Hou ZS, Xu JX (2003) Freeway traffic density control using iterative learning control approach. In: Proceedings of the 2003 IEEE intelligent transportation systems (ITS), pp 1081–1086

  14. Bu XH, Liang J, Hou ZS, Chi RH (2020) Data-driven terminal iterative learning consensus for nonlinear multi-agent systems with output saturation. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.2995600

    Article  Google Scholar 

  15. Bu XH, Hou ZS, Zhang HW (2018) Data-driven multiagent systems consensus tracking using model free adaptive control. IEEE Trans Neural Netw Learn Syst 29(5):1514–1524

    Article  MathSciNet  Google Scholar 

  16. Li XH, Ruan X (2020) Monotonic convergence and robustness of higher-order gain-adaptive iterative learning control. Int J Robust Nonlinear Control. https://doi.org/10.1002/rnc.4978

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu J, Ruan X, Zheng YS (2020) Iterative learning control for discrete-time systems with full learnability. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3028388

    Article  Google Scholar 

  18. Bu XH, Zhu PP, Hou ZS, Liang JQ (2020) Finite-time consensus for linear multi-agent systems using data-driven terminal ILC. IEEE Trans Circuits Syst II Express Briefs 67(10):2029–2033

    Article  Google Scholar 

  19. Chen YQ, Moore K (2002) Harnessing the non-repetitiveness in iterative learning control. In: Proceedings of the 41th IEEE conference on decision and control (CDC), pp 3350–3355

  20. Butcher M, Karimi A (2010) Linear parameter-varying iterative learning control with application to a linear motor system. IEEE-ASME Trans Mechatron 15(3):412–420

    Article  Google Scholar 

  21. Hou ZS, Yan JW, Xu JX, Li ZJ (2012) Modified iterative-learning-control-based ramp metering strategies for freeway traffic control with iteration-dependent factors. IEEE Trans Intell Transp Syst 13(2):606–618

    Article  Google Scholar 

  22. Liu T, Gao FR (2010) Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties. Chem Eng Sci 65:6134–6144

    Article  Google Scholar 

  23. Shi J, Gao FR, Wu TJ (2005) Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system. J Process Control 15(8):907–924

    Article  Google Scholar 

  24. Meng DY, Moore KL (2014) On robust iterative learning control against iteration-varying uncertain plant parameters. In: 2014 American control conference (ACC), Portland, pp 4255–4261

  25. Meng DY, Moore KL (2017) Convergence of iterative learning control for SISO nonrepetitive systems subject to iteration-dependent uncertainties. Automatica 79:167–177

    Article  MathSciNet  Google Scholar 

  26. Meng DY, Moore KL (2017) Robust iterative learning control for nonrepetitive uncertain systems. IEEE Trans Autom Control 62(2):907–913

    Article  MathSciNet  Google Scholar 

  27. Janssens P, Pipeleers G, Swevers J (2013) A data-driven constrained norm-optimal iterative learning control framework for LTI systems. IEEE Trans Control Syst Technol 21(2):546–551

    Article  Google Scholar 

  28. Oh SK, Lee JM (2015) Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories. J Process Control 36:64–78

    Article  Google Scholar 

  29. Yu QX, Hou ZS (2016) Data-driven predictive iterative learning control for a class of multiple-input and multiple-output nonlinear systems. Trans Inst Meas Control 38(3):266–281

    Article  Google Scholar 

  30. Chi RH, Huang B, Wang DW, Zhang RK, Feng YJ (2016) Data-driven optimal terminal iterative learning control with initial value dynamic compensation. IET Control Theory Appl 10(12):1357–1364

    Article  MathSciNet  Google Scholar 

  31. Geng Y, Ruan X (2020) Adaptive iterative learning control for switched discrete-time systems with stochastic measurement noise. Trans Inst Meas Control 42(2):259–271

    Article  Google Scholar 

  32. Yu M, Li CY (2017) Robust adaptive iterative learning control for discrete-time nonlinear systems with time-iteration-varying parameters. IEEE Trans Syst Man Cybern Syst 47(7):1737–1745

    Article  Google Scholar 

  33. Liu J, Chen WS, Ruan X, Zheng YS (2020) Data-based iterative learning mechanism for unknown input-output coupling parameters/matrices. Int J Robust Nonlinear Control 30:1275–1297

    Article  MathSciNet  Google Scholar 

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Funding

This work was funded by National Science Foundation of China (61973338), Natural Science Basic Research Plan in Shaanxi Province of China (2020JQ-831), Scientific Research Program Funded by Shaanxi Provincial Education Department (20JK0642) and Key Research and Development Plan in Shaanxi Province of China (2020GY-072).

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Sciences, Xi’an Polytechnic University, Xi’an, 710048, China

    Yan Geng & Xuan Yang

  2. Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Xiaoe Ruan

  3. Research Center for Applied Mathematics and Interdisciplinary Sciences, Beijing Normal University at Zhuhai, Zhuhai, 519087, China

    Qinghua Zhou

Authors
  1. Yan Geng
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  2. Xiaoe Ruan
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  3. Qinghua Zhou
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  4. Xuan Yang
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Correspondence to Yan Geng.

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Geng, Y., Ruan, X., Zhou, Q. et al. Robust adaptive iterative learning control for nonrepetitive systems with iteration-varying parameters and initial state. Int. J. Mach. Learn. & Cyber. 12, 2327–2337 (2021). https://doi.org/10.1007/s13042-021-01313-9

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  • DOI: https://doi.org/10.1007/s13042-021-01313-9

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