Abstract
In this paper, an overview of fractional-order iterative learning control (FOILC) is presented including main developments of this field since 2001. Many theoretical and experimental results are provided to show the advantages of FOILC such as the improvement of transient and steady-state performances. Some unique characters of fractional-order operators are illustrated to show the new features and techniques of FOILC. A number of unsolved problems are briefly presented.
Similar content being viewed by others
Notes
If either G(s) or H(s) is related to s ν, where ν is a non-integer constant, then (8) becomes a FOILC learning law. Moreover, in this case T u =I, so that lim k→∞ e k (t)=0 for all t∈[0,t f ].
References
Arimoto, S., Kawamura, S., Miyazaki, F.: Bettering operation of robots by learning. J. Robot. Syst. 1(2), 123–140 (1984)
Chen, Y.Q., Moore, K.L., Ahn, H.-S.: Iterative Learning Control. Encyclopedia of the Science of Learning. Springer, New York (2012). Book chapter of Seel, N. M. (Editor in Chief)
Ahn, H.-S., Moore, K.L., Chen, Y.Q.: Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems. Springer, New York, London (2007)
Sun, M.X., Wang, D.W.: Higher relative degree nonlinear systems with ILC using lower-order differentiations. Asian J. Control 4(1), 38–48 (2008)
Norrlof, M.: Disturbance rejection using an ILC algorithm with iteration varying filters. Asian J. Control 6(3), 432–438 (2008)
Lee, F.-S., Chien, C.-J., Wang, J.-C., Liu, J.-J.: Application of a model-based iterative learning technique to tracking control of a piezoelectric system. Asian J. Control 7(1), 29–37 (2008)
Ye, Y., Wang, D.W., Zhang, B., Wang, Y.: Simple LMI based learning control design. Asian J. Control 11(1), 74–77 (2009)
Xu, J.-X.: The frontiers of iterative learning control—Part I. J. Syst. Control Inf. 46(2), 563–594 (2002)
Xu, J.-X.: The frontiers of iterative learning control—Part II. J. Syst. Control Inf. 46(5), 233–243 (2002)
Xu, J.-X., Tan, Y.: Robust optimal design and convergence properties analysis of iterative learning control approaches. Automatica 38(11), 1867–1880 (2001)
Han, C., Qu, Z.H., Kaloust, J.H.: Nonlinar iterative learning for a class of nonlinear systems based on Lyapunov’s direct method. In: Proceedings of American Control Conference, pp. 3024–3028. IEEE, New York (1995)
Frueh, M., Rogers, E.: Nonlinear iterative learning by an adaptive Lyapunov technique. Int. J. Control 73(10), 858–870 (2000)
Sulikowski, B., Galkowski, K., Rogers, E., Owens, D.H.: PI Control of discrete linear repetitive processes. Automatica 42(5), 877–880 (2006)
Sulikowski, B., Galkowski, K., Rogers, E.: PI output feedback control of differential linear repetitive processes. Automatica 44(5), 1442–1445 (2008)
Wang, H.B., Wang, Y.: Iterative learning control for nonlinear systems with uncertain state delay and arbitrary initial error. J. Control Theory Appl. 9(4), 541–547 (2011)
Meng, D.Y., Jia, Y.M., Du, J.P., Yuan, S.Y.: Feedback iterative learning control for time-delay systems based on 2D analysis approach. J. Control Theory Appl. 8(4), 457–463 (2010)
Yin, C.K., Xu, J.X., Hou, Z.S.: A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters. IEEE Trans. Autom. Control 55(1), 2665–2670 (2010)
Arif, M., Ishihara, T., Inooka, H.: Incorporation of experience in iterative learning controllers using locally weighted learning. Automatica 37(6), 881–888 (2001)
Moore, K.L., Lashhab, F.: Iteration-domain closed-loop frequency response shaping for discrete-repetitive processes. In: Proceedings of American Control Conference, pp. 1284–1289. IEEE, New York (2010)
Fine, B.T., Mishra, S., Tomizuka, M.: Model inverse based iterative learning control using finite impulse response approximations. In: Proceedings of American Control Conference, pp. 931–936. IEEE, New York (2009)
Mishra, S.: Fundamental Issues in Iterative Learning Controller Design: Convergence, Robustness, and Steady State Performance. Ph.D. Dissertation, University of California, Berkeley (2008)
Ahn, H.-S., Chen, Y.Q., Moore, K.L.: Iterative learning control: Brief survey and categorization. IEEE Trans. Syst. Man Cybern., Part C, Appl. Rev. 37(6), 1099–1121 (2007)
Rogers, E.: Iterative learning control—from Hilbert spaces to robotics to healthcare engineering. United Kingdom Automatic Control Conference Annual Lecture (2007). URL: http://eprints.ecs.soton.ac.uk/14560/
Le, F., Markovsky, I., Freeman, C.T., Rogers, E.: Identification of electrically stimulated muscle models of stroke patients. Control Eng. Pract. 18(4), 396–407 (2010)
Chen, Y.Q., Moore, K.L.: On Dα-type iterative learning control. In: Proceedings of IEEE Conference on Decision and Control, vol. 5, pp. 4451–4456. IEEE, New York (2001)
Ye, Y., Tayebi, A., Liu, X.: All-pass filtering in iterative learning control. Automatica 45(1), 257–264 (2009)
Li, Y., Chen, Y.Q., Ahn, H.-S.: Fractional-order iterative learning control for fractional-order linear systems. Asian J. Control 13(1), 1–10 (2011)
Lazarevic, M.P.: PD α-type iterative learning control for fractional LTI system. In: Proceedings of International Congress of Chemical and Process Engineering, p. 0359. Czech Society of Chemical Engineering, Praha (2004)
Sabatier, J., Agrawal, O.P., Tenreiro Machado, J.A. (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)
Li, Y., Chen, Y.Q., Ahn, H.-S.: A generalized fractional-order iterative learning control. In: Proceedings of IEEE Conference on Decision and Control and European Control Conference, pp. 5356–5361. IEEE, New York (2011)
Papoulis, A.: The Fourier Integral and its Applications. McGraw-Hill, New York (1962)
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Bien, Z., Huh, K.M.: Higher-order iterative learning control algorithm. IEE Proc., Control Theory Appl. 136(3), 105–112 (1989)
Chen, Y.Q., Wen, C.Y.: Iterative Learning Control—Convergence, Robustness and Applications. Springer, London (1999)
Ruan, X., Bien, Z., Wang, Q.: Convergence properties of iterative learning control processes in the sense of the Lebesgue-p norm. Asian J. Control 14(4), 1095–1107 (2012)
Moore, K.L., Dahleh, M., Bhattacharyya, S.P.: Iterative learning control: a survey and new results. J. Robot. Syst. 9(5), 563–594 (1992)
Moore, K.L., Chen, Y.Q., Ahn, H.-S.: Iterative learning control: A tutorial and big picture view. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 2352–2357 (2006)
Goh, C.J.: A frequency domain analysis of learning control. ASME J. Dyn. Syst. Meas. Control 116(4), 781–786 (1994)
Hideg, L.M., Judd, R.P.: Frequency domain analysis of learning systems. In: Proceedings of the 27th IEEE Conference on Decisions and Control, pp. 586–591 (1988)
Lan, Y.-H., He, L.-J.: P-type iterative learning control of fractional order nonlinear time-delay systems. In: Proceedings of the 24th Chinese Control and Decision Conference, pp. 1027–1031 (2012)
Lazarevic, M.P.: PD α-type iterative learning control for fractional LTI system. In: Proceedings of the 4th International Carpathian Control Conference, pp. 869–872 (2003)
Lazarevic, M.P.: Iterative learning control for fractional linear time delay system: PI β D α type. In: Proceedings of the 17th International Congress of Chemical and Process Engineering, p. 5.19 (2006)
Li, Y., Chen, Y.Q., Ahn, H.-S.: Fractional order iterative learning control. In: Proceedings of the ICROS-SICE International Joint Conference, pp. 2106–3110 (2009)
Lazarevic, M.P.: Iterative learning feedback control for nonlinear fractional order system—PD α type. In: Proceedings of the 4th IFAC Workshop Fractional Differentiation and its Applications (2012). Paper No. 259
Li, Y., Ahn, H.-S., Chen, Y.Q.: Iterative learning control of a class of fractional order nonlinear systems. In: Proceedings of the IEEE International Symposium on Intelligent Control, Part of IEEE Multi-Conference on Systems and Control, pp. 779–782 (2010)
Li, Y., Chen, Y.Q., Ahn, H.-S.: Fractional order iterative learning control for fractional order linear systems. Asian J. Control 13(1), 54–63 (2011)
Li, Y., Chen, Y.Q., Ahn, H.-S.: On the PD α-type iterative learning control for the fractional-order nonlinear systems. In: Proceedings of the American Control Conference, pp. 4320–4325 (2011)
Li, Y., Chen, Y.Q., Ahn, H.-S.: Convergence analysis of fractional-order iterative learning control. Control Theory Appl. 29(8), 1027–1031 (2012)
Xu, J.-X., Hou, Z.-S.: On learning control: the state of the art and perspective. Acta Autom. Sin. 31(6), 943–955 (2005)
Lee, H.-S., Bien, Z.: A note on convergence property of iterative learning controller with respect to sup norm. Automatica 33(8), 1591–1593 (1997)
Li, H.S., Huang, J.C., Liu, D., Zhang, J.H., Teng, F.L.: Design of fractional order iterative learning control on frequency domain. In: Proceedings of the IEEE International Conference on Mechatronics and Automation, pp. 2056–2060 (2011)
Xu, M., Tan, W.: Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions. Sci. China Ser. G, Phys. Astron. 46(2), 145–157 (2003)
Sheng, H., Chen, Y.Q., Qiu, T.S.: Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications. Springer, London, New York (2012)
Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5(4), 367–386 (2002)
Podlubny, I., Heymans, N.: Physical interpretation of initial conditions for fractional differential equations with Riemann–Liouville fractional derivatives. Rheol. Acta 45(5), 765–772 (2006)
Zhang, F.R., Li, C.P.: Remarks on the initialization of Caputo derivative. In: Proceedings of the IEEE/ASME 8th IEEE/ASME International Conference on Mechatronics and Embedded Systems and Applications, pp. 325–329 (2012)
Xu, J.-X., Yan, R.: On initial conditions in iterative learning control. IEEE Trans. Autom. Control 50(9), 1349–1354 (2005)
Lan, Y.H.: Iterative learning control with initial state learning for fractional order nonlinear systems. Comput. Math. Appl. (2012). doi:10.1016/j.camwa.2012.03.086
Song, X.N., Tejado, I., Chen, Y.Q.: Remote stabilization for fractional-order systems via communication networks. In: Proceedings of the American Control Conference, pp. 6698–6703. IEEE, New York (2010)
Chen, Y.Q.: Ubiquitous fractional order controls? In: Proceedings of the 2nd IFAC Symposium on Fractional Derivatives and Applications, vol. 2 (2006). doi:10.3182/20060719-3-PT-4902.00081
Westerlund, S., Ekstam, L.: Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is Supported by National Natural Science Foundation of China (61075092, 61104009), Natural Science Foundation of Shandong Province (ZR2011FM011, ZR2010AM007), Independent Innovation Foundation of Shandong University (2010TB022, 2011JC017).
Rights and permissions
About this article
Cite this article
Li, Y., Chen, Y., Ahn, HS. et al. A Survey on Fractional-Order Iterative Learning Control. J Optim Theory Appl 156, 127–140 (2013). https://doi.org/10.1007/s10957-012-0229-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10957-012-0229-9