Skip to main content
SpringerLink
Log in
Book cover

Control Subject to Computational and Communication Constraints pp 151–179Cite as

Event-Triggered State-Feedback via Dynamic High-Gain Scaling for Nonlinearly Bounded Triangular Dynamics

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 475))

Abstract

This paper focuses on the construction of Event-Triggered state feedback laws. The approach followed is a high-gain approach. The event which triggers an update of the control law is based on a dynamical system in which the state is the high-gain parameter. This approach allows to design a control law ensuring convergence to the origin for nonlinear systems with triangular structure and a specific upper bound on the nonlinearities which is more general than a linear growth condition.

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   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Notes

  1. 1.

    If Z is a symmetric matrix, \(\lambda _{\max }(Z)\) and \(\lambda _{\min }(Z)\) denote its largest and its smallest eigenvalue, respectively.

References

  1. Abdelrahim, M., Postoyan, R., Daafouz, J., Nesic, D.: Input-to-state stabilization of nonlinear systems using event-triggered output feedback controllers. In: 14th European Control Conference, ECC’15 (2015)

    Google Scholar 

  2. Alur, R., Arzen, K.-E., Baillieul, J., Henzinger, T.A., Hristu-Varsakelis, D., Levine, W.S.: Handbook of Networked and Embedded Control Systems. Springer Science & Business Media (2007)

    Google Scholar 

  3. Ames, W.F., Pachpatte, B.G.: Inequalities for Differential and Integral Equations, vol. 197. Academic press, San Diego (1997)

    Google Scholar 

  4. Andrieu, V., Praly, L.: A unifying point of view on output feedback designs. In: 7th IFAC Symposium on Nonlinear Control Systems, pp. 8–19 (2007)

    Article  Google Scholar 

  5. Andrieu, V., Tarbouriech, S.: Global asymptotic stabilization for a class of bilinear systems by hybrid output feedback. IEEE Trans. Autom. Control. 58(6), 1602–1608 (2013)

    Article  MathSciNet  Google Scholar 

  6. Andrieu, V., Praly, L., Astolfi, A.: Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems. Syst. Control. Lett. 58(9), 652–663 (2009)

    Article  MathSciNet  Google Scholar 

  7. Andrieu, V., Praly, L., Astolfi, A.: High gain observers with updated gain and homogeneous correction terms. Automatica 45(2), 422–428 (2009)

    Article  MathSciNet  Google Scholar 

  8. Andrieu, V., Nadri, M., Serres, U., Vivalda, J.-C.: Self-triggered continuous-discrete observer with updated sampling period. Automatica 62, 106–113 (2015)

    Article  MathSciNet  Google Scholar 

  9. Anta, A., Tabuada, P.: To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans. Autom. Control. 55(9), 2030–2042 (2010)

    Article  MathSciNet  Google Scholar 

  10. Aström, K.J., Wittenmark, B.: Computer-controlled systems. Prentice Hall, Englewood Cliffs (1997)

    Google Scholar 

  11. Dabroom, A.M., Khalil, H.K.: Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Trans. Autom. Control. 46(11), 1712–1725 (2001)

    Article  MathSciNet  Google Scholar 

  12. Dinh, T.-N., Andrieu, V., Nadri, M., Serres, U.: Continuous-discrete time observer design for lipschitz systems with sampled measurements. IEEE Trans. Autom. Control. 60(3), 787–792 (2015)

    Article  MathSciNet  Google Scholar 

  13. Girard, A.: Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Autom. Control. 60(7), 1992–1997 (2015)

    Article  MathSciNet  Google Scholar 

  14. Heemels, W.P.M.H., Johansson, K.-H., Tabuada, P.: An introduction to event-triggered and self-triggered control. In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), pp. 3270–3285 (2012)

    Google Scholar 

  15. Heemels, W.P.M.H., Johansson, K.-H., Tabuada, P.: Event-triggered and self-triggered control. In: Baillieul, J., Samad, T. (eds.) Encyclopedia of Systems and Control, pp. 1–10. Springer, London (2014)

    Google Scholar 

  16. Krishnamurthy, P., Khorrami, F.: Dynamic high-gain scaling: state and output feedback with application to systems with iss appended dynamics driven by all states. IEEE Trans. Autom. Control. 49(12), 2219–2239 (2004)

    Article  MathSciNet  Google Scholar 

  17. Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities: Theory and applications. Vol. I: Ordinary Differential Equations. Mathematics in Science and Engineering, vol. 55-I. Academic Press, New York (1969)

    MATH  Google Scholar 

  18. Marchand, N., Durand, S., Castellanos, J.F.G.: A general formula for event-based stabilization of nonlinear systems. IEEE Trans. Autom. Control. 58(5), 1332–1337 (2013)

    Article  Google Scholar 

  19. Mazenc, F., Andrieu, V., Malisoff, M.: Design of continuous-discrete observers for time-varying nonlinear systems. Automatica 57, 135–144 (2015)

    Article  MathSciNet  Google Scholar 

  20. Nesic, D., Teel, A.R., Kokotović, P.V.: Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Syst. Control. Lett. 38(45), 259–270 (1999)

    Article  MathSciNet  Google Scholar 

  21. Peralez, J., Andrieu, V., Nadri, M., Serres, U.: Self-triggered control via dynamic high-gain scaling. In: IFAC proceedings Volumes (IFAC-PapersOnLine), vol. 10 (2016)

    Article  Google Scholar 

  22. Peralez, J., Andrieu, V., Nadri, M., Serres, U.: Event-triggered output feedback stabilization via dynamic high-gain scaling. IEEE Trans. Autom. Control. (2018)

    Google Scholar 

  23. Postoyan, R., Tabuada, P., Nesic, D., Anta, A.: A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Autom. Control. 60(4), 982–996 (2015)

    Article  MathSciNet  Google Scholar 

  24. Praly, L.: Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate. IEEE Trans. Autom. Control. 48(6), 1103–1108 (2003)

    Article  MathSciNet  Google Scholar 

  25. Qian, C., Du, H.: Global output feedback stabilization of a class of nonlinear systems via linear sampled-data control. IEEE Trans. Autom. Control. 57(11), 2934–2939 (2012)

    Article  MathSciNet  Google Scholar 

  26. Seuret, A., Prieur, C., Marchand, N.: Stability of non-linear systems by means of event-triggered sampling algorithms. IMA J. Math. Control. Inf. (2013)

    Google Scholar 

  27. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control. 52(9), 1680–1685 (2007)

    Article  MathSciNet  Google Scholar 

  28. Villarreal-Cervantes, M.G., Guerrero-Castellanos, J.F., Ramrez-Martnez, S., Snchez-Santana, P.: Stabilization of a (3,0) mobile robot by means of an event-triggered control. ISA Trans. 58, 605–613 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Univ. Lyon, Université Claude Bernard Lyon 1, CNRS, LAGEP UMR 5007, 43 bd du 11 novembre 1918, 69100, Villeurbanne, France

    J. Peralez, V. Andrieu, M. Nadri & U. Serres

Authors
  1. J. Peralez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Andrieu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Nadri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. U. Serres
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Andrieu .

Editor information

Editors and Affiliations

  1. LAAS-CNRS, Université de Toulouse, Toulouse, France

    Sophie Tarbouriech

  2. Laboratoire des Signaux et Systèmes, CNRS, CentraleSupélec, Université Paris-Sud, Université Paris-Saclay, Gif-sur-Yvette, France

    Antoine Girard

  3. CNRS, Centrale Lille, UMR 9189—Centre de Recherche en Informatique Signal et Automatique de Lille (CRIStAL), Université Lille, Lille, France

    Laurentiu Hetel

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Peralez, J., Andrieu, V., Nadri, M., Serres, U. (2018). Event-Triggered State-Feedback via Dynamic High-Gain Scaling for Nonlinearly Bounded Triangular Dynamics. In: Tarbouriech, S., Girard, A., Hetel, L. (eds) Control Subject to Computational and Communication Constraints. Lecture Notes in Control and Information Sciences, vol 475. Springer, Cham. https://doi.org/10.1007/978-3-319-78449-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-78449-6_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78448-9

  • Online ISBN: 978-3-319-78449-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation