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Nonlinear Sampled-Data Stabilization with Delays

  • Salvatore Monaco
  • Dorothée Normand-CyrotEmail author
  • Mattia Mattioni
Chapter
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 10)

Abstract

In this work, how sampling can be instrumental for stabilizing nonlinear dynamics with delays is discussed through several approaches developed by the authors in a comparative perspective with respect to the existing literature. Performances and computational aspects are illustrated through academic examples.

References

  1. 1.
    Astolfi, A., Karagiannis, D., Ortega, R.: Nonlinear and Adaptive Control with Applications. Springer Publishing Company, Berlin (2008)CrossRefGoogle Scholar
  2. 2.
    Astolfi, A., Ortega, R.: Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans. Autom. Control 48(4), 590–606 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bekiaris-Liberis, N., Krstic, M.: Compensation of state-dependent input delay for nonlinear system. IEEE Trans. Autom. Control 58(2), 275–289 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Califano, C., Marquez-Martinez, L., Moog, C.: Linearization of time-delay systems by input-output injection and output transformation. Automatica 49(6), 1932–1940 (2013)Google Scholar
  5. 5.
    Celsi, L., Bonghi, R., Monaco, S., Normand-Cyrot, D.: On the exact steering of finite sampled nonlinear dynamics with input delays. IFAC-PapersOnLine 48(11), 674–679 (2015)CrossRefGoogle Scholar
  6. 6.
    Di Giamberardino, P., Monaco, S., Normand-Cyrot, D.: Why multirate sampling is instrumental for control design purpose: the example of the one-leg hopping robot. In: Proceedings of the 41st IEEE CDC, vol. 3, pp. 3249–3254 (2002)Google Scholar
  7. 7.
    Di Giamberardino, P., Monaco. S., Normand-Cyrot, D.: On equivalence and feedback equivalence to finitely computable sampled models. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 5869–5874.  https://doi.org/10.1109/CDC.2006.377699 (2006)
  8. 8.
    Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46(2), 421–427 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fridman, E.: Introduction to Time-Delay Systems: Analysis and Control. Systems & Control: Foundations & Applications (2014)Google Scholar
  10. 10.
    Karafyllis, I., Krstic, M.: Nonlinear stabilization under sampled and delayed measurements, and with inputs subject to delay and zero-order hold. IEEE Trans. Autom. Control 57(5), 1141–1154 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Karafyllis, I., Krstic, M.: Numerical schemes for nonlinear predictor feedback. Math. Control Signals Syst. 26, 519–546 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Krstic, M.: Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Springer, Berlin (2009)CrossRefGoogle Scholar
  13. 13.
    Krstic, M.: Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans. Autom. Control 55(2), 287–303 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Mattioni, M., Monaco, S., Normand-Cyrot, D.: Digital stabilization of strict feedback dynamics through immersion and invariance. In: Proceedings of the IFAC MICNON, pp. 1085–1090. St Petersbourg (2015)Google Scholar
  15. 15.
    Mattioni, M., Monaco, S., Normand Cyrot, D.: Sampled-data stabilisation of a class of state-delayed nonlinear dynamics. In: 54th IEEE Conference on Decision and Control (CDC), pp. 5695–5700 (2015)Google Scholar
  16. 16.
    Mattioni, M., Monaco, S., Normand-Cyrot, D.: Further results on sampled-data stabilization of time-delay systems. In: Proceedings of the 20th IFAC World Congress, pp. 14915–14920 (2017)Google Scholar
  17. 17.
    Mattioni, M., Monaco, S., Normand-Cyrot, D.: Immersion and invariance stabilization of strict-feedback dynamics under sampling. Automatica 76, 78–86 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Mattioni, M., Monaco, S., Normand-Cyrot, D.: Sampled-data reduction of nonlinear input-delayed dynamics. IEEE Control Syst. Lett. 1(1), 116–121 (2017)CrossRefGoogle Scholar
  19. 19.
    Mazenc, F., Fridman, E.: Predictor-based sampled-data exponential stabilization through continuous-discrete observers. Automatica 63, 74–81 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mazenc, F., Malisoff, M., Dinh, T.N.: Robustness of nonlinear systems with respect to delay and sampling of the controls. Automatica 49(6), 1925–1931 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Mazenc, F., Niculescu, S., Bekaik, M.: Backstepping for nonlinear systems with delay in the input revisited. SIAM J. Control Optim. 49(6), 2239–2262 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mazenc, F., Normand-Cyrot, D.: Reduction model approach for linear systems with sampled delayed inputs. IEEE Trans. Autom. Control 58(5), 1263–1268 (2013)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Michiels, W., Niculescu, S.: Stability, Control, and Computation for Time-delay Systems: An Eigenvalue Based Approach. Advances in Design and Control. SIAM Society for Industrial and Applied Mathematics, Philadelphia (2014)CrossRefGoogle Scholar
  24. 24.
    Monaco, S., Normand-Cyrot, D., Mattioni, M.: Sampled-data stabilization of nonlinear dynamics with input delays through immersion and invariance. IEEE Trans. Autom. Control 62(5), 2561–2567 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Monaco, S., Normand-Cyrot, D., Tanasa, V.: Digital stabilization of input delayed strict feedforward dynamics. In: Proceedings of the 51st IEEE-CDC, Maui, Hawaii, pp. 7535–7540 (2012)Google Scholar
  26. 26.
    Monaco, S., Normand-Cyrot, D., Tiefensee, F.: Sampled-data stabilization; a PBC approach. IEEE Trans. Autom. Control 56, 907–912 (2011)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pepe, P.: Stabilization in the sample-and-hold sense of nonlinear retarded systems. SIAM J. Control Optim. 52(5), 3053–3077 (2014)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Pepe, P.: Robustification of nonlinear stabilizers in the sample-and-hold sense. J. Frankl. Inst. 352(10), 4107–4128 (2015)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Pepe, P., Fridman, E.: On global exponential stability preservation under sampling for globally lipschitz time-delay systems. Automatica 82(8), 295–300 (2017)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Respondek, W., Tall, I.: Feedback equivalence of nonlinear control systems: a survey on formal approaches, pp. 137–262. CRC Press, Boca Raton.  https://doi.org/10.1201/9781420027853.ch4 (2005). Accessed from 18 Oct 2016
  31. 31.
    Tanasa, V., Monaco, S., Normand-Cyrot, D.: Digital stabilization of finite sampled nonlinear dynamics with delays: the unicycle example. In: Proceedings of the ECC’13, pp. 2591–2596 (2013)Google Scholar
  32. 32.
    Tanasa, V., Monaco, S., Normand-Cyrot, D.: Backstepping control under multi-rate sampling. IEEE Trans. Autom. Control 61(5), 1208–1222 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Yalcin, Y., Astolfi, A.: Immersion and invariance adaptive control for discrete time systems in strict feedback form. Syst. Control Lett. 61(12), 1132–1137 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Salvatore Monaco
    • 1
  • Dorothée Normand-Cyrot
    • 2
    Email author
  • Mattia Mattioni
    • 3
  1. 1.Dipartimento di Ingegneria Informatica, Automatica e GestionaleDIAG Università di Roma “La Sapienza”RomaItaly
  2. 2.Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506) CNRS; 3, rue Joliot CurieGif-sur-YvetteFrance
  3. 3.DIAG (Università di Roma ‘La Sapienza’)RomeItaly

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