Skip to main content
SpringerLink
Log in
Book cover

Recent Results on Nonlinear Delay Control Systems pp 95–112Cite as

State Estimation and Control of Nonlinear Systems with Large and Variable Measurement Delays

  • Chapter
  • First Online:

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 4))

Abstract

This chapter deals with the problem of output feedback control of nonlinear systems affected by time-varying measurement delay. A control law is presented, which is made of an observer-controller cascade where the controller is a classic state-linearizing scheme, and the observer is a high-gain observer of chain-type. It is shown that under suitable conditions on the system, the observer is globally exponentially convergent, and the replacement of the true state with the observer state in the control law results in an exponentially stabilizing feedback scheme. The main limitation with a single observer is the presence of a delay bound that depends on the Lipschitz constant of the nonlinear system. To overcome this limitation it is possible to resort to a chain of observers that, at the cost of a growing realization space and convergence time, can in principle allow to compensate any delay. This design is straightforward when the delay is known and constant but its extension to time-varying delays requires special attention, in particular when the delay is not continuous with respect to time, as it frequently happens in the applications. We therefore introduce a classification of delay functions with respect to the available output information and illustrate how to design the cascade of elementary observers to solve the state reconstruction problem. We also characterize the class of delay functions for which this approach fails to provide a viable implementation.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Ahmed-Ali, T., Cherrier, E., M’Saad, M.: Cascade high gain observers for nonlinear systemms with delayed output. In: Proceedings of the 48th Conference on Decision and Control, pp. 8226–8231 (2009)

    Google Scholar 

  2. Ahmed-Ali, T., Cherrier, E., Lamnabhi-Lagarrigue, F.: Cascade high gain predictor for a class of nonlinear systems. IEEE Trans. Autom. Control 57(1), 221–226 (2012)

    Article  MathSciNet  Google Scholar 

  3. Andrieu, V., Praly, L.: On the existence of a Kazantis-Kravaris/Luemberger observer. SIAM J. Control Optim. 45(2), 432–456 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Byrnes, C.I., Isidori, A.: Nonlinear internal models for output regulation. IEEE Trans. Autom. Control 49(12), 2244–2247 (2004)

    Article  MathSciNet  Google Scholar 

  5. Cacace, F., Germani, A., Manes, C.: An observer for a class of nonlinear systems with time varying observation delay. Syst. Control Lett. 59(5), 305–312 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cacace, F., Germani, A., Manes, C.: An exponential observer with delay-dependant gain for a class of nonlinear systems with time-varying measurement delay. In: Proceedings of the IEEE Conference on Decision and Control, pp. 2364–2369 (2013)

    Google Scholar 

  7. Cacace, F., Germani, A., Manes, C.: A chain approach for state observation of a class of MIMO nonlinear systems with time-varying output delays. In: Proceedings of the 11th IFAC Workshop on Time-Delay Systems, pp. 541–546 (2013)

    Google Scholar 

  8. Cacace, F., Germani, A., Manes, C.: A chain observer for nonlinear systems with multiple time-varying measurement delays. SIAM J. Control Optim. 52(3), 1862–1885 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ciccarella, G., Dalla Mora, M., Germani, A.: A Luenberger-like observer for nonlinear systems. Int. J. Control 57(3), 537–556 (1993)

    Google Scholar 

  10. Dalla Mora, M., Germani, A., Manes, C.: Design of state observers from a drift-observability property. IEEE Transac. Autom. Control 45(8), 1536–1540 (2000)

    Google Scholar 

  11. Ding, Z.: Output feedback stabilization of systems with nonlinearity of unmeasured states. In: Proceedings of the IEEE Conference on Decision and Control, pp. 5414–5419 (2008)

    Google Scholar 

  12. Fridman, E.: Output regulation of nonlinear systems with delay. Syst. Control Lett. 50(2), 81–93 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Germani, A., Manes, C., Pepe, P.: A new approach to state observation of nonlinear systems with delayed output. IEEE Trans. Autom. Control 47(1), 96–101 (2002)

    Article  MathSciNet  Google Scholar 

  14. Germani, A., Manes, C., Pepe, P.: Input-output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability. Int. J. Robust Nonlinear Control 13(9), 909–937 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Germani, A., Manes, C., Pepe, P.: Observer-based stabilizing control for a class of nonlinear retarded systems. In: Sipahi, R., Vyhlidal, T., Niculescu, S.-I., Pepe, P. (eds.) Time Delay Systems: Methods, Applications and New Trends, pp. 331–342. Springer, Berlin Heidelberg (2012)

    Chapter  Google Scholar 

  16. Hua, C., Guan, X., Shi, P.: Robust stabilization of a class of nonlinear time-delay systems. Appl. Math. Comput. 155(3), 737–752 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Isidori, A.: Nonlinear Control Systems: An Introduction. Springer-Verlag, Berlin (1995)

    Book  MATH  Google Scholar 

  18. Jankovic, M.: Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems. IEEE Trans. Autom. Control 46(7), 1048–1060 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Karafyllis, I., Jiang, Z-P.: Necessary and sufficient Lyapunov-like conditions for robust nonlinear stabilization. ESAIM: Control, Optim. Calc. Var. 16(4), 887–928 (2010)

    Google Scholar 

  20. Kazantzis, N., Wright, R.: Nonlinear observer design in the presence of delayed output measurements. Syst. Control Lett. 54(9), 877–886 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kravaris, C., Wright, R.: Dead time compensation for nonlinear chemical processes. AlChE J. 35(9), 1535–1542 (1989)

    Article  Google Scholar 

  22. Kreisselmeier, G., Engel, R.: Nonlinear observer for autonomous Lipschitz continuous systems. IEEE Trans. Autom. Control 48(3), 451–464 (2003)

    Article  MathSciNet  Google Scholar 

  23. Krener, A., Xiao, M.: Erratum: Nonlinear observer design in the Siegel domain. SIAM J. Control Optim. 43(1), 377–378 (2004)

    Article  MathSciNet  Google Scholar 

  24. Lien, C.-H.: Global exponential stabilization for several classes of uncertain nonlinear systems with time-varying delay. Nonlinear Dyn. Syst. Theor. 4(1), 15–30 (2004)

    MATH  MathSciNet  Google Scholar 

  25. Maggiore, M., Passino, K.: A separation principle for a class of non uniformly completely observable systems. IEEE Trans. Autom. Control 48(7), 1122–1133 (2003)

    Article  MathSciNet  Google Scholar 

  26. Marconi, L., Praly, L., Isidori, A.: Output stabilization via nonlinear Luenberger observers. SIAM J. Control Optim. 45(6), 2277–2298 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. Márquez-Martinez, L., Moog, C.: Input-output feedback linearization of time-delay systems. IEEE Trans. Autom. Control 49(5), 781–785 (2004)

    Article  Google Scholar 

  28. Márquez-Martinez, L., Moog, C., Velasco-Villa, M.: Observability and observers for nonlinear systems with time-delays. In: Proceedings of the 2nd IFAC Workshop on Time Delay Systems, pp. 52–58 (2000)

    Google Scholar 

  29. Meadows, E., Rawlings, J.: Model predictive control. In: Henson, M., Seborg, D. (eds.) Nonlinear Process Control, pp. 233–310. Prentice Hall, Englewood Cliffs, NJ (1997)

    Google Scholar 

  30. Mikheev, Y., Sobolev, V., Fridman, E.: Asymptotic analysis of digital control systems. Autom. Remote Control 49(9), 1175–1180 (1988)

    MATH  MathSciNet  Google Scholar 

  31. Oguchi, T., Watanabe, A., Nakamizo, T.: Input-output linearization of retarded non-linear systems by using an extension of Lie derivative. Int. J. Control 75(8), 582–590 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Smith, O.: Closer control of loops with dead-time. Chem. Eng. Prog. 53(5), 217–219 (1957)

    Google Scholar 

  33. Tatiraju, S., Soroush, M., Ogunnaike, B.: Multirate nonlinear state estimation with application to a polymerization reactor. AlChE J. 45(4), 769–776 (1999)

    Article  Google Scholar 

  34. Van Assche, V., Ahmed-Ali, T., Hann, C., Lamnabhi-Lagarrigue, F.: High gain observer design for nonlinear systems with time varying delayed measurement. In: Proceedings of the 18th IFAC World Congress, pp. 692–696 (2011)

    Google Scholar 

  35. Zhang, X., Cheng, Z.: Global stabilization of a class of time-delay nonlinear systems. Int. J. Syst. Sci. 36(8), 461–468 (2005)

    Article  MATH  Google Scholar 

  36. Zhang, X., Zhang, C., Cheng, Z.: Asymptotic stabilization via output feedback for nonlinear systems with delayed output. Int. J. Syst. Sci. 37(9), 599–607 (2006)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Università Campus Biomedico di Roma, Rome, Italy

    Filippo Cacace

  2. Università dell’Aquila, L’Aquila, Italy

    Alfredo Germani & Costanzo Manes

Authors
  1. Filippo Cacace
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfredo Germani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Costanzo Manes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Filippo Cacace .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Iasson Karafyllis

  2. Department of Mathematics, Louisiana State University (LSU), Baton Rouge, Louisiana, USA

    Michael Malisoff

  3. CNRS-CentraleSupélec-Université Paris Sud, EPI Inria “DISCO”, Laboratory of Signals and Systems (L2S, UMR CNRS 8506), Gif-sur-Yvette, France

    Frederic Mazenc

  4. Department of Information Engineering, Computer Science, and Mathematics, University of L’Aquila, L’Aquila, Italy

    Pierdomenico Pepe

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Cacace, F., Germani, A., Manes, C. (2016). State Estimation and Control of Nonlinear Systems with Large and Variable Measurement Delays. In: Karafyllis, I., Malisoff, M., Mazenc, F., Pepe, P. (eds) Recent Results on Nonlinear Delay Control Systems. Advances in Delays and Dynamics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-18072-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-18072-4_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18071-7

  • Online ISBN: 978-3-319-18072-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation