Fractional order PDα-type ILC for linear continuous time-delay switched system with disturbance measurement and uncertainties noise

Document Type : Research Paper

Author

Indira Gandhi Govt. College Pandaria, Distt.- Kabirdham, Hemchand Yadav Vishwavidyalaya Durg, Chhattisgarh, India - 491559.

Abstract

This study investigates the efficacy of a novel PDα-type fractional-order iterative learning control (FOILC) approach for a class of fractional-order linear continuous-time delaying switched systems. The approach is evaluated in terms of Lp norm performance, aiming to mitigate the challenges associated with time delays in repetitive regulation of fractional-order linear systems. The generalised Young inequality of the convolution integral is used to leverage the resilience of the PDα-type approach in the iteration domain when the systems are perturbed by constrained external disturbances. We next analyse the convergence of the techniques for noise-free systems. The results demonstrate that it is feasible to guarantee both convergence and robustness over the duration of the experiment in certain situations. We study the convergence of error for the proposed class of fractional-order linear continuous-time delaying switched systems.

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References

[1] S. Arimoto, S. Kawamura and F. Miyazaki, Bettering operation of robots by learning, J. Robotic Syst., 1(2) (1984), 123-140.
[2] X. H. Bu, X. S. Hou and F. S. Yu, Iterative learning control for a class of linear continuous-time switched systems, Control Theory and Applications, 29(8) (2012), 1051-1056. (in Chinese).
[3] X. H. Bu, Z. S. Hou, F. S. Yu, et al., Iterative learning control for a class of non-linear switched systems, IET Control Theory and Applications, 7(3) (2013), 470-481.
[4] Y. Q. Chen and K. L. Moore, On D  -type iterative learning control, Decision and Control Proceedings of the 40th IEEE Conference on IEEE, Florida, USA, (2001), 4451-4456.
[5] Y. Chenchen and W. Jing, Closed-loop PD  -type iterative learning control for fractional nonlinear systems with time- delay, Proc. of 11th Asian Control Conference, IEEE, 723-728, 2017.
[6] O. Dewangan, Convergence analysis of proportional-derivative -type ILC for linear continuous constant time delay switched systems with observation noise and state uncertainties, Journal of Hyperstructures, 12(2)(2023), 351-365.
[7] K. Diethelm and N. J. FORD, Analysis of fractional differential equation, Journal of Mathematics and applications, 265(2) (2002), 229-248.
[8] Z. Kejun1 and P. Guohua, Robustness of iterative learning control for a class of fractional-order linear continuous-time switched systems in the sense of Lp norm, Journal of Systems Engineering and Electronics, 30(4) (2019), 783-791.
[9] Y. H. Lanand and X. Liu, Second-order P-type iterative learning control for fractional order nonlinear time-delay systems, International Journal of Computational Science and Engineering, 13(1) (2016), 48-55.
[10] Y. H. Lan and L. J. He, P-type iterative learning control of fractional order nonlinear time-delay systems, Proc. of 24th Chinese Control and Decision Conference, IEEE, (2012), 1027-1031.
[11] Y. H. Lan and Y. Zhou, D  -type iterative learning control for fractional order linear time-delay systems, Asian Journal of Control, 3(15) (2013), 669-677.
[12] Y. H. Lan and Y. Zhou, High-order D -type iterative learning control for fractional-order nonlinear time-delay systems, J. Optimiz. Theory App., 156(1) (2013), 153-166.
[13] M. Lazarevic, B. Cvetkovic and P. Mandic, Closed-loop iterative learning control for fractional-order linear singular time-delay system: PD -type, Scienti c Technical Review, 2(68) (2018), 17-25.
[14] M. Lazarevic , N. Durovic B. Cvetkovic P. Mandic and M. Cajic , PD  -type iterative learning control for fractional- order singular time-delay system, Proc. of 29th Chinese Control And Decision Conference, IEEE, 1905-1910, 2017.
[15] Y. Li, L. Zhang and B. Hu, PD -type iterative learning control for fractional delay systems, Journal of Physics: IOP Conf. Series: Journal of Physics: Conf. Series, 1053(2018), 012135.
[16] Y. Li, Y. Q. Chen and H. S. Ahn, Fractional-order iterative learning control for fractional-order linear systems, Asian Journal of Control, 1(13) (2011), 54-63.
[17] K. H. Park and Z. Bien, Intervalized iterative learning control for monotonic convergence in the sense of sup-norm, Int. J. Control, 78(15) (2005), 1218-1227.
[18] I. Podlubny, Fractional differential equations, San Diego: Academic Press, 1999. 
[19] S. Y. QIN and Y. H. SONG, The theory of hybrid control systems and its application perspective in electric power systems, Proc. of the International Conference on Info-Tech and Info-Net, 4 (2001), 85-94.
[20] X. Ruan, J. B. Lian and H. Z. Wu, Convergence of iterative learning control with feedback information in the sense of Lebesgue-p norm, Acta Automatica Sinica, 37(4) (2011), 513-516. (in Chinese).
[21] Z. Sun and S. S. Ge, Switched linear systems: control and design, IEEE Trans. on Automatic Control, 51(9) (2006), 1585-1586.
[22] F. A. Wyczaled, Hybrid electric vehicles: year 2000 status, IEEE Aerospace and Electronics Systems Magazine, 16(3) (2001), 15-25.
[23] X. Yang and X. Ruan, Analysis of iterative learning control for a class of linear discrete-time switched systems, Abstract and Applied Analysis, Vol. 2015, Hindawi.
[24] L. Yan and J. Wei, Fractional order nonlinear systems with delay in iterative learning control, Appl. Math. Comput., 257 (2015), 546-552.
Journal of Hyperstructures
Volume 13, Issue 2
2024
Pages 305-320

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