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Insights on Event-Triggered Control for Linear Systems Subject to Norm-Bounded Uncertainty

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Control Subject to Computational and Communication Constraints

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

Abstract

The chapter deals with the design of Event-Triggered rules to stabilize a class of uncertain linear control systems where the uncertainty affecting the plant is assumed to be norm-bounded. The event-triggering rule uses only local information, namely the control updates are generated only by the output signals available to the controller. The proposed approach combines a hybrid framework to describe the closed-loop system with techniques based on looped functionals. The suggested design conditions are formulated in terms of linear matrix inequalities (LMIs), ensuring global robust asymptotic stability of the closed-loop system. A tunable parameter allows guaranteeing an adjustable dwell-time property of the solutions. The effectiveness of the approach is evaluated on an example taken from the literature.

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References

  1. Abdelrahim, M., Postoyan, R., Daafouz, J., Nešić, D. Co-design of output feedback laws and event-triggering conditions for linear systems. In: 53rd IEEE Conference on Decision and Control, (CDC 2014), pp. 3560–3565. Los Angeles (CA), USA (2014)

    Google Scholar 

  2. Abdelrahim, M., Postoyan, R., Daafouz, J., Nes̆ić, D. Stabilization of nonlinear systems using event-triggered output feedback laws. In: 21st International Symposium on Mathematical Theory of Networks and Systems. Groningen, The Netherlands (2014)

    Google Scholar 

  3. Årzén, K.-E. A simple event-based PID controller. In: Proceedings of the 14th IFAC World Congress, vol. 18, pp. 423–428. Beijing, China (1999)

    Google Scholar 

  4. Aström, K.J. Event based control. In: Analysis and Design of Nonlinear Control Systems, pp. 127–147. Springer, Berlin (2008)

    Google Scholar 

  5. Åström, K.J., Bernhardsson, B.: Comparison of periodic and event based sampling for first-order stochastic systems. In: Proceeding 14th IFAC World Congress, vol. 11, pp. 301–306, Beijing, China (1999)

    Google Scholar 

  6. Briat, C., Seuret, A.: A looped-functional approach for robust stability analysis of linear impulsive systems. Syst. Control Lett. 61(10), 980–988 (2012)

    Article  MathSciNet  Google Scholar 

  7. Chen, T., Francis, B.A.: Optimal Sampled-data Control Systems. Springer, Berlin, Germany (1995)

    Book  Google Scholar 

  8. Cloosterman, M.B.G., Hetel, L., Van De Wouw, N., Heemels, W.P.M.H., Daafouz, J., Nijmeijer, H.: Controller synthesis for networked control systems. Automatica 46(10), 1584–1594 (2010)

    Article  MathSciNet  Google Scholar 

  9. Donkers, M.C.F., Heemels, W.P.M.H.: Output-based event-triggered control with guaranteed-gain and improved and decentralized event-triggering. IEEE Trans. Autom. Control 57(6), 1362–1376 (2012)

    Article  MathSciNet  Google Scholar 

  10. Fichera, F., Prieur, C., Tarbouriech, S., Zaccarian, L.: A Convex Hybrid \(\cal{H}_\infty \) synthesis with guaranteed convergence rate. In: 51st IEEE Conference on Decision and Control, pp. 4217–4222. Maui (HI), USA (2012)

    Google Scholar 

  11. Fichera, F., Prieur, C., Tarbouriech, S., Zaccarian, L.: Using Luenberger observers and Dwell-time logic for feedback hybrid loops in continuous-time control systems. Int. J. Robust Nonlinear Control 23, 1065–1086 (2013)

    Article  MathSciNet  Google Scholar 

  12. Fridman, E., Seuret, A., Richard, J.-P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1141–1446 (2004)

    Article  MathSciNet  Google Scholar 

  13. Goebel, R., Sanfelice, R., Teel, A.R.: Hybrid dynamical systems. IEEE Control Syst. Mag. 29(2), 28–93 (2009)

    Article  MathSciNet  Google Scholar 

  14. Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, Princeton (2012)

    Book  Google Scholar 

  15. Heemels, W.P.M.H., Donkers, M.C.F., Teel, A.R.: Periodic event-triggered control for linear systems. IEEE Trans. Autom. Control 58(4), 847–861 (2013)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  17. Heemels, W.P.M.H., Teel, A.R., van de Wouw, N., Nes̆ić, D.: Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55(8), 1781–1796 (2010)

    Article  MathSciNet  Google Scholar 

  18. Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)

    Article  Google Scholar 

  19. Hetel, L., Fiter, C., Omran, H., Seuret, A., Fridman, E., Richard, J.-P., Niculescu, S.-I.: Recent developments on the stability of systems with aperiodic sampling: an overview. Automatica 76, 309–335 (2017)

    Article  MathSciNet  Google Scholar 

  20. Lunze, J., Lehmann, D.: A state-feedback approach to event-based control. Automatica 46(1), 211–215 (2010)

    Article  MathSciNet  Google Scholar 

  21. Mazo, M., Anta, A., Tabuada, P.: An ISS self-triggered implementation of linear controllers. Automatica 46(8), 1310–1314 (2010)

    Article  MathSciNet  Google Scholar 

  22. Naghshtabrizi, P., Hespanha, J.P., Teel, A.R.: Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control Lett. 57(5), 378–385 (2008)

    Article  MathSciNet  Google Scholar 

  23. Nešić, D., Teel, A.R.: A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Trans. Autom. Control 49(7), 1103–1122 (2004)

    Article  MathSciNet  Google Scholar 

  24. Petersen, I.R.: A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8, 351–356 (1987)

    Article  MathSciNet  Google Scholar 

  25. Postoyan, R., Girard, A.: Triggering mechanism using freely selected sensors for linear time-invariant systems. In: 54th IEEE Conference on Decision and Control, pp. 4812–4817. Osaka, Japan (2015)

    Google Scholar 

  26. Postoyan, R., Tabuada, P., Nes̆ić, D., Anta, A.: Event-triggered and self-triggered stabilization of distributed networked control systems. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 2565–2570. Orlando (FL), USA (2011)

    Google Scholar 

  27. Prieur, C., Goebel, R., Teel, A.R.: Hybrid feedback control and robust stabilization of nonlinear systems. IEEE Trans. Autom. Control 52(11), 2103–2117 (2007)

    Article  MathSciNet  Google Scholar 

  28. Prieur, C., Seuret, A., Tarbouriech, S., Zaccarian, L.: Event-triggered control via reset control systems framework. In: IFAC Symposium on Nonlinear Control Systems (NOLCOS). Monterey, CA, USA (2016)

    Google Scholar 

  29. Prieur, C., Tarbouriech, S., Zaccarian, L.: Guaranteed stability for nonlinear systems by means of a hybrid loop. In: IFAC Symposium on Nonlinear Control Systems (NOLCOS), pp. 72–77. Bologna, Italy (2010)

    Article  Google Scholar 

  30. Prieur, C., Tarbouriech, S., Zaccarian, L.: Lyapunov-based hybrid loops for stability and performance of continuous-time control systems. Automatica 49(2), 577–584 (2013)

    Article  MathSciNet  Google Scholar 

  31. Seuret, A.: A novel stability analysis of sampled-data systems with applications to multi-rate sampling and packet loss. Automatica 48(1), 177–182 (2012)

    Article  MathSciNet  Google Scholar 

  32. Seuret, A., Prieur, C.: Event-based sampling algorithms based on a Lyapunov function. In: 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 6128–6133. Orlando (FL), USA (2011)

    Google Scholar 

  33. Seuret, A., Prieur, C., Tarbouriech, S., Zaccarian, L., Teel, A.R.: A nonsmooth hybrid invariance principle applied to robust event-triggered design. Available: https://hal.laas.fr/hal-01526331 (2017) [Online]

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

    Article  MathSciNet  Google Scholar 

  35. Tallapragada, P., Chopra, N.: Event-triggered dynamic output feedback control for LTI systems. In: 51st IEEE Conference on Decision and Control, pp. 6597–6602. Maui (HI), USA (2012)

    Google Scholar 

  36. Tarbouriech, S., Seuret, A., Gomes da Silva Jr., J.M., Sbarbaro, D. Observer-based event-triggered control co-design for linear systems. IET Control Theory Appl. 10(18), 2466–2473 (2016)

    Article  MathSciNet  Google Scholar 

  37. Wang, X., Lemmon, M.D.: Event design in event-triggered feedback control systems. In: 47th IEEE Conference on Decision and Control, pp. 2105–2110. Cancun, Mexico (2008)

    Google Scholar 

  38. Zampieri, S.: A survey of recent results in networked control systems. In: Proceedings of the \(17^{th}\) IFAC World Congress, pp. 2886–2894. Seoul, Korea (2008)

    Google Scholar 

  39. Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice Hall Inc., Upper Saddle River, New Jersey (1996)

    Google Scholar 

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Author information

Authors and Affiliations

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

    S. Tarbouriech

  2. University Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, France

    C. Prieur

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

    A. Seuret & L. Zaccarian

  4. Dipartimento di Ingegneria Industriale, University of Trento, Trento, Italy

    L. Zaccarian

Authors
  1. S. Tarbouriech
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  2. A. Seuret
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  3. C. Prieur
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  4. L. Zaccarian
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Corresponding author

Correspondence to S. Tarbouriech .

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

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Tarbouriech, S., Seuret, A., Prieur, C., Zaccarian, L. (2018). Insights on Event-Triggered Control for Linear Systems Subject to Norm-Bounded Uncertainty. 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_9

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  • DOI: https://doi.org/10.1007/978-3-319-78449-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78448-9

  • Online ISBN: 978-3-319-78449-6

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