Switching-iterative learning control method for discrete-time switching system

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Abstract

In this paper, we propose a new monotonically convergent switching iterative learning control for a class of linear discrete time switched system. It is assumed that the considered switched systems are operated during a finite time interval repetitively, and then the iterative learning control scheme can be introduced. After the switched system is transformed into a 2D repetitive system, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived by using a Lyapunov functional approach and a quadratic performance function. It is shown that if certain LMIs are met, the tracking error \(l_2\) norm converges monotonically to zero between (subsystem/iteration), while the switching learning gains could be determined directly by solving the LMIs.The integrated design of this SILC scheme is transformed into a robust monotonic stabilizability problem (RMS) of an uncertain switched system. A numerical simulation example is established shown the effectiveness of the proposed method .

Keywords

Switched systems Iterative learning control (ILC) Quadratic function \(l_2 \) norm Tracking control Polytopic uncertainties Linear matrix inequality 

References

  1. 1.
    Liu Y, Sun LY, Lu BC, Dai MZ (2010) Feedback control of networked switched fuzzy time-delay systems based on observer. ICIC Express Lett 4(6(B)):2369–2376Google Scholar
  2. 2.
    Attia SB, Salhi S, Ksouri M (2012) Static switched output feedback stabilization for linear discrete-time switched systems. Int J Innov Comput Inf Control (IJICIC) 8(5(A)):3203–3213Google Scholar
  3. 3.
    Attia SB, Salhi S, Ksouri M (2009) LMI Formulation for static output feedback design of discrete-time switched systems. J Control Sci Eng (JSCE) vol 8, article ID 362920, 7 pagesGoogle Scholar
  4. 4.
    Attia SB, Salhi S, Ksouri M (june 2009) Mode-Independent state feedback design for discrete switched linear. In: European conference on modelling and simultion, ECMS, Madrid, pp 6–9Google Scholar
  5. 5.
    Attia SB, Salhi S, Ksouri M (2009) Improved LMI formulation for robust dynamic output feedback controller design of discrete-time switched systems via switched Lyapunov function. In: The 3rd international conference on signals, circuits and systems (SCS09), 6–8 November, Djerba, TunisiaGoogle Scholar
  6. 6.
    Dridi J, Attia SB, Salhi S, Ksouri M (2012) Repetitive processes based iterative learning control designed by LMIs. Int Sch Res Netw ISRN Appl Math.  https://doi.org/10.5402/2012/365927 MATHGoogle Scholar
  7. 7.
    Zhifu L, Peng Y, Yueming H, Qiwei G (2012) LMI approach to robust monotonically convergent iterative learning control for uncertain linear discrete-time systems. In: Procedings of the 31th Chinesse control conference, Hefeai, china, vol8, pp 25–27Google Scholar
  8. 8.
    Ouerfelli HE, Dridi J, Attia SB, Salhi S (2014) Iterative learning control for discret time switched system. In: International conference on control, engineering information technology (CEIT14), pp 310–321Google Scholar
  9. 9.
    Paszke W, Gakowski K, Rogers E (October 2012) Repetitive process based iterative learning control design using frequency domain analysis. In: Proceedings of the the 2012 IEEE multi-conference on systems and control (MSC 2012), Dubrovnik, Croatia, p 36Google Scholar
  10. 10.
    Scherer C, Gahinet P, Chilali M (1997) Multi-objective output-feedback control via LMI optimization. IEEE Trans Autom Control 42(7):896–911CrossRefMATHGoogle Scholar
  11. 11.
    Paszke W, Rogers E, Gałkowski K (September 2011) Design of robust iterative learning control schemes in a finite frequency range. In: Proceedings of the international workshop on multidimensional (nD) systems, nDS 2011, pp. 1–6, Poitiers, France, 5–7Google Scholar
  12. 12.
    Reithmerier E, Leitmann G (2003) Robust vibration control of dynamical systems based on the derivative of the state. Arch Appl Mech 72:856–864MATHGoogle Scholar
  13. 13.
    Bu X-H, Yu F-H, Hou Z-S, Wang F-Z (2013) Iterative learning control for a class of linear discrete-time switched systems. Acta Autom Sin 39(9):1564–1569MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ouerfelli HE, Dridi J, Attia SB, Salhi S (2015) Iterative learning tracking control for discret time switched. Int J Sci Res Eng Technol (IJSET) 3(3):43–46Google Scholar
  15. 15.
    Moore KL, Dahleh M, Bhattacharyya SP (1992) Iterative learning control: a survey and new results. J Robot Syst 9(5):563–594CrossRefMATHGoogle Scholar
  16. 16.
    Gakowski K, Rogers D, Owens H (2007) Control systems theory and applications for linear repetitive processes. Lecture notes in control and information sciences, vol 349. Springer, BerlinGoogle Scholar
  17. 17.
    Zhang P, Ding SX (2007) on some norms of linear discrete-time periodic systems. Lecture notes in control and information sciences, vol 48. Springer, Berlin, pp 118–125Google Scholar
  18. 18.
    Deyuan M, Yingmin J, Junping D, Fashan Y (2012) Monotonically convergent ILC systems designed using bounded real lemma. Int J Syst Sci 43(11):20622071MathSciNetMATHGoogle Scholar
  19. 19.
    Liberzon D, Hespanha JP, Morse AS (1999) Stability of switched linear systems: a Lie-algebraic condition. Syst Control Lett 37(3):117–122CrossRefMATHGoogle Scholar
  20. 20.
    West X, Road X, Shaan X (2015) A PD-Type iterative learning control for a class of switched discrete-time systems with model uncertainties and external noises. Dis Dyn Nat Soc vol 2015, Article ID 410292, 11 pagesGoogle Scholar
  21. 21.
    Menga D, Jiaab Y, Duc J, Yud F (2012) Monotonically convergent ILC systems designed using bounded real lemma. Int J Syst Sci 43(11):20622071Google Scholar
  22. 22.
    Leyva R, Martnez-Salamero L, Valderrama-Blavi H, Maix J, Giral R, Guinjoan F (2001) Linear state-feedback control of a boost converter for large-signal stability. IEEE Trans Circuits Syst Fundam Theory Appl 48(04):418–424CrossRefGoogle Scholar
  23. 23.
    Hui BX, Shan Y Fa, Sheng HZ, Zhong WF (2013) Iterative learning control for a class of linear discrete-time switched systems. Acta Autom Sin 39(9):1564–1569MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Analysis and Control and conception of Systems (LACCS), National Engineering School of TunisUniversity of Tunis El ManarTunisTunisia

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