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Volume 12 Issue 10
Oct.  2025

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  >  12(10): 2067-2081
I. Hussain, X. Ruan, C. Liu, and B. Li, “Data-driven adaptive P-type iterative learning control for linear discrete time singular systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2067–2081, Oct. 2025. doi: 10.1109/JAS.2024.125040
Citation: I. Hussain, X. Ruan, C. Liu, and B. Li, “Data-driven adaptive P-type iterative learning control for linear discrete time singular systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 10, pp. 2067–2081, Oct. 2025. doi: 10.1109/JAS.2024.125040
shu

Data-Driven Adaptive P-Type Iterative Learning Control for Linear Discrete Time Singular Systems

doi: 10.1109/JAS.2024.125040
Funds:  This work was supported by the National Natural Science Foundation of China (619733380)
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    Abstract
  • Aiming at the pulse response sequence of a kind of repetitive linear discrete-time singular systems unavailable, the paper explores a data-driven adaptive iterative learning control (DDAILC) strategy that interacts with the pulse response iterative correction (PRIC). The mechanism is to formulate the correction performance index as a linear summation of the quadratic correction error of the pulse response and the quadratic tracking error. The correction algorithm of the pulse response arrives and the correction error goes down in a monotonic way. It also discusses the conditional relationship between the declining rate of the correction error and the correction ratio. A DDAILC algorithm is designed by means of substituting the exact pulse response of the gain-optimized iterative learning control (GOILC) with its approximated one updated in the correction algorithm. The convergences regarding tracking error and correction error are obtained monotonically. Finally, numerical simulation verifies the validity and effectiveness.

     

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  • [1]
    D. Luenberger, “Dynamic equations in descriptor form,” IEEE Trans. Autom. Control, vol. 22, no. 3, pp. 312–321, 1977. doi: 10.1109/TAC.1977.1101502
    [2]
    Z. Wang, Y. Shen, X. Zhang, and Q. Wang, “Observer design for discrete-time descriptor systems: An LMI approach,” Systems and Control Letters, vol. 61, no. 6, pp. 683–687, 2012. doi: 10.1016/j.sysconle.2012.03.006
    [3]
    G.-R. Duan, Analysis and Design of Descriptor Linear Systems. New York: Springer, 2010.
    [4]
    T. Iwasaki and G. Shibata, “LPV system analysis via quadratic separator for uncertain implicit systems,” IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1195–1208, 2001. doi: 10.1109/9.940924
    [5]
    G. Verghese, B. Lévy, and T. Kailath, “A generalized state-space for singular systems,” IEEE Trans. Autom. Control, vol. 26, no. 4, pp. 811–831, 1981. doi: 10.1109/TAC.1981.1102763
    [6]
    A. Ailon, “Controllability of generalized linear time-invariant systems,” IEEE Trans. Autom. Control, vol. 32, no. 5, pp. 429–432, 1987. doi: 10.1109/TAC.1987.1104626
    [7]
    R. Newcomb and B. Dziurla, “Some circuits and systems applications of semi-state theory,” Circuits, Systems and Signal Processing, vol. 8, no. 3, pp. 235–260, 1989. doi: 10.1007/BF01598413
    [8]
    H. H. Rosenbrock, “Structural properties of linear dynamical systems,” Int. J. Control, vol. 20, no. 2, pp. 191–202, 1974. doi: 10.1080/00207177408932729
    [9]
    S. Xu and J. Lam, Robust Control and Filtering of Singular Systems. Berlin: Springer-Verlag, 2006.
    [10]
    S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” J. Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984. doi: 10.1002/rob.4620010203
    [11]
    Y. Chen and C. Wen, Iterative Learning Control: Convergence, Robustness and Applications. London: Springer, 1999.
    [12]
    D. A. Bristow, M. Tharayil, and A. G. Alleyne, “A survey of iterative learning control,” IEEE Control Systems Magazine, vol. 26, no. 3, pp. 96–114, 2006. doi: 10.1109/MCS.2006.1636313
    [13]
    J.-X. Xu, “A survey on iterative learning control for nonlinear systems,” Int. J. Control, vol. 84, no. 7, pp. 1275–1294, 2011. doi: 10.1080/00207179.2011.574236
    [14]
    D. Shen, “Iterative learning control with incomplete information: A survey,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 885–901, 2018. doi: 10.1109/JAS.2018.7511123
    [15]
    H.-S. Ahn, Y. Chen, and K. L. Moore, “Iterative learning control: Brief survey and categorization,” IEEE Trans. Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 37, no. 6, pp. 1099–1121, 2007. doi: 10.1109/TSMCC.2007.905759
    [16]
    Y. Wang, F. Gao, and F. J. Doyle III, “Survey on iterative learning control, repetitive control, and run-to-run control,” J. Process Control, vol. 19, no. 10, pp. 1589–1600, 2009. doi: 10.1016/j.jprocont.2009.09.006
    [17]
    P. Gu, S. Tian, and Q. Liu, “Iterative learning control for a class of discrete-time singular systems,” Advances in Difference Equations, vol. 2018, no. 1, pp. 1–14, 2018. doi: 10.1186/s13662-017-1452-3
    [18]
    S. Tian, Q. Liu, X. Dai, and J. Zhang, “A PD-type iterative learning control algorithm for singular discrete systems,” Advances in Difference Equations, vol. 2016, no. 1, pp. 1–9, 2016. doi: 10.1186/s13662-015-0739-5
    [19]
    P. Gu, S. Tian, and Q. Liu, “Closed-loop iterative learning control for discrete singular systems with fixed initial shift,” J. Systems Science and Complexity, vol. 32, no. 2, pp. 577–587, 2019. doi: 10.1007/s11424-018-7221-x
    [20]
    X.-S. Dai, X.-Y. Zhou, S.-P. Tian, and H.-T. Ye, “Iterative learning control for MIMO singular distributed parameter systems,” IEEE Access, vol. 5, pp. 24094–24104, 2017. doi: 10.1109/ACCESS.2017.2768480
    [21]
    X. Dai and X. Zhou, “Mixed PD-type iterative learning control algorithm for a class of parabolic singular distributed parameter systems,” IEEE Access, vol. 9, pp. 12180–12190, 2021. doi: 10.1109/ACCESS.2021.3050486
    [22]
    J. Liu, H. Tian, S. Tian, and X. Li, “Iterative learning control for discrete singular systems with randomly varying trial lengths,” in Proc. IEEE 7th Data Driven Control and Learning Systems Conf., Enshi, China, pp. 97–101, 2018.
    [23]
    F. Piao, Q. Zhang, and Z. Wang, “Iterative learning control for uncertain singular system,” in Proc. IEEE Int. Conf. Information Acquisition, Weihai, China, pp. 1469–1474, 2006.
    [24]
    S. S. Alaviani, “Iterative learning control based on 2D system theory for singular linear continuous-time systems,” in Proc. IEEE Int. Conf. Control Applications, Hyderabad, India, pp. 855–858, 2013.
    [25]
    S. S. Alaviani, “2D system based iterative learning control for linear singular discrete-time systems,” in Proc. IEEE 60th Int. Midwest Symposium on Circuits and Systems, pp. 1093–1096, IEEE, 2017.
    [26]
    Q. Liu, S. Tian, and P. Gu, “Iterative learning control for a class of singular impulsive systems,” Int. J. Systems Science, vol. 49, no. 7, pp. 1383–1390, 2018. doi: 10.1080/00207721.2018.1453954
    [27]
    Q. Liu, S. Tian, and P. Gu, “P-type iterative learning control algorithm for a class of linear singular impulsive systems,” J. Franklin Institute, vol. 355, no. 9, pp. 3926–3937, 2018. doi: 10.1016/j.jfranklin.2018.03.011
    [28]
    P. Gu and S. Tian, “Analysis of iterative learning control for one-sided Lipschitz nonlinear singular systems,” J. Franklin Institute, vol. 356, no. 1, pp. 196–208, 2019. doi: 10.1016/j.jfranklin.2018.10.014
    [29]
    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, 2017.
    [30]
    P. Gu, S. Tian, and Q. Liu, “Iterative learning control for discrete singular time-delay systems,” IMA J. Mathematical Control and Information, vol. 36, no. 2, pp. 623–637, 2019. doi: 10.1093/imamci/dnx061
    [31]
    M. Togai and O. Yamano, “Analysis and design of an optimal learning control scheme for industrial robots: A discrete system approach,” in Proc. 24th IEEE Conf. Decision and Control, Fort Lauderdale, USA, pp. 1399–1404, 1985.
    [32]
    N. Amann, D. H. Owens, and E. Rogers, “Iterative learning control using optimal feedback and feedforward actions,” Int. J. Control, vol. 65, no. 2, pp. 277–293, 1996. doi: 10.1080/00207179608921697
    [33]
    B. Chu and D. H. Owens, “Accelerated norm-optimal iterative learning control algorithms using successive projection,” Int. J. Control, vol. 82, no. 8, pp. 1469–1484, 2009. doi: 10.1080/00207170802512824
    [34]
    K. L. Barton and A. G. Alleyne, “A norm optimal approach to time-varying ILC with application to a multi-axis robotic testbed,” IEEE Trans. Control Systems Technology, vol. 19, no. 1, pp. 166–180, 2010.
    [35]
    B. Chu and D. H. Owens, “Iterative learning control for constrained linear systems,” Int. J. Control, vol. 83, no. 7, pp. 1397–1413, 2010. doi: 10.1080/00207171003758752
    [36]
    X. Ge, J. L. Stein, and T. Ersal, “Frequency-domain analysis of robust monotonic convergence of norm-optimal iterative learning control,” IEEE Trans. Control Systems Technology, vol. 26, no. 2, pp. 637–651, 2017.
    [37]
    D. H. Owens, C. T. Freeman, and B. Chu, “Multi-variable norm optimal iterative learning control with auxiliary optimisation,” Int. J. Control, vol. 86, no. 6, pp. 1026–1045, 2013. doi: 10.1080/00207179.2013.771822
    [38]
    R. Chi, Z. Hou, S. Jin, and B. Huang, “Computationally-light non-lifted data-driven norm-optimal iterative learning control,” Asian J. Control, vol. 20, no. 1, pp. 115–124, 2018. doi: 10.1002/asjc.1569
    [39]
    S. Gunnarsson and M. Norrlöf, “On the design of ILC algorithms using optimization,” Automatica, vol. 37, no. 12, pp. 2011–2016, 2001. doi: 10.1016/S0005-1098(01)00154-6
    [40]
    D. H. Owens and K. Feng, “Parameter optimization in iterative learning control,” Int. J. Control, vol. 76, no. 11, pp. 1059–1069, 2003. doi: 10.1080/0020717031000121410
    [41]
    J. J. Hätönen, D. H. Owens, and K. L. Moore, “An algebraic approach to iterative learning control,” Int. J. Control, vol. 77, no. 1, pp. 45–54, 2004. doi: 10.1080/00207170310001638614
    [42]
    D. H. Owens, B. Chu, and M. Songjun, “Parameter-optimal iterative learning control using polynomial representations of the inverse plant,” Int. J. Control, vol. 85, no. 5, pp. 533–544, 2012. doi: 10.1080/00207179.2012.658867
    [43]
    I. Hussain, X. Ruan, and Y. Liu, “Convergence characteristics of iterative learning control for discrete-time singular systems,” Int. J. Systems Science, vol. 52, no. 2, pp. 217–237, 2021. doi: 10.1080/00207721.2020.1824030
    [44]
    Y. Yuan, Q. He, X. Luo, and M. Shang, “A multilayered-and-randomized latent factor model for high-dimensional and sparse matrices,” IEEE Trans. Big Data, vol. 8, no. 3, pp. 784–794, 2020.
    [45]
    R.-C. Roman, R.-E. Precup, E.-L. Hedrea, S. Preitl, I. A. Zamfirache, C.-A. Bojan-Dragos, and E. M. Petriu, “Iterative feedback tuning algorithm for tower crane systems,” Procedia Computer Science, vol. 199, pp. 157–165, 2022. doi: 10.1016/j.procs.2022.01.020
    [46]
    R.-C. Roman, R.-E. Precup, E. M. Petriu, and M. Muntyan, “Fictitious reference iterative tuning of discrete-time model-free control for tower crane systems,” Studies in Informatics and Control, vol. 32, no. 1, pp. 5–14, 2023. doi: 10.24846/v32i1y202301
    [47]
    R.-E. Precup, R.-C. Roman, and A. Safaei, Data-Driven Model-Free Controllers. New York: CRC Press, 2021.
    [48]
    P. Janssens, G. Pipeleers, and J. Swevers, “A data-driven constrained norm-optimal iterative learning control framework for LTI systems,” IEEE Trans. Control Systems Technology, vol. 21, no. 2, pp. 546–551, 2012.
    [49]
    R. Chi, Y. Liu, Z. Hou, and S. Jin, “Data-driven terminal iterative learning control with high-order learning law for a class of non-linear discrete-time multiple-input–multiple output systems,” IET Control Theory and Applications, vol. 9, no. 7, pp. 1075–1082, 2015. doi: 10.1049/iet-cta.2014.0754
    [50]
    R. Chi, Z. Hou, S. Jin, and B. Huang, “An improved data-driven point-to-point ILC using additional on-line control inputs with experimental verification,” IEEE Trans. Systems, Man, and Cybernetics: Systems, vol. 49, no. 4, pp. 687–696, 2017.
    [51]
    R. Chi, B. Huang, Z. Hou, and S. Jin, “Data-driven high-order terminal iterative learning control with a faster convergence speed,” Int. J. Robust and Nonlinear Control, vol. 28, no. 1, pp. 103–119, 2018. doi: 10.1002/rnc.3861
    [52]
    C. Zeng, D. Shen, and J. Wang, “Adaptive learning tracking for uncertain systems with partial structure information and varying trial lengths,” J. Franklin Institute, vol. 355, no. 15, pp. 7027–7055, 2018. doi: 10.1016/j.jfranklin.2018.07.031
    [53]
    Y. Geng, X. Ruan, and H.-S. Ahn, “Data-driven networked optimal iterative learning control for discrete linear time-varying systems with one-operation Bernoulli-type communication delays,” Discrete Dynamics in Nature and Society, vol. 2017, no. 1, pp. 1–12, 2017.
    [54]
    Y. Geng and X. Ruan, “Iterative learning identification and control for point-to-point tracking of linear time-varying systems with unknown parameters and stochastic noise,” Trans. Institute of Measurement and Control, vol. 40, no. 13, pp. 3834–3845, 2018. doi: 10.1177/0142331217733036
    [55]
    I. Hussain, X. Ruan, C. Liu, and Y. Liu, “Linearly monotonic convergence and robustness of P-type gain-optimized iterative learning control for discrete-time singular systems,” IEEE Access, vol. 9, no. 0, pp. 58337–58350, 2021.
    [56]
    X. Ruan and Y. Liu, “Monotone convergence rate of norm-optimal-gain-arguable iterative learning control for LDTI systems,” Asian J. Control, vol. 24, no. 2, pp. 920–941, 2022. doi: 10.1002/asjc.2498
    [57]
    R. Chi, D. Wang, Z. Hou, and S. Jin, “Data-driven optimal terminal iterative learning control,” J. Process Control, vol. 22, no. 10, pp. 2026–2037, 2012. doi: 10.1016/j.jprocont.2012.08.001
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