Skip to main content

Event-Triggered Sliding Mode Control for Nonlinear Systems

  • Chapter
  • First Online:
Event-Triggered Sliding Mode Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 139))

Abstract

In this chapter, event-triggered SMC for nonlinear systems is presented. Similar design approaches are used for nonlinear system like LTI systems in the earlier chapter. As a preliminary, first SMC is designed for continuous-time system that yields stable sliding motion. Then, this control is used in designing the event-triggered SMC for nonlinear systems. A sufficient condition for the stability and existence of practical sliding mode are also given. In practical applications, delays in control implementation are unavoidable that may the affect system performance. The event-triggering strategy is also developed by considering such delays into account.

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

Access this chapter

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
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Institutional subscriptions

References

  1. A.F. Filippov, Differential Equations With Discontinuous Right-Hand Sides (Kluwer Academic Publishers, Dordrecht, 1988)

    Book  MATH  Google Scholar 

  2. H. Khalil, Nonlinear Systems, 3rd edn. (Prentice-Hall, Upper Saddle River, NJ, 2002)

    MATH  Google Scholar 

  3. V.I. Utkin, Sliding Modes and Their Applications in Variable Structure Systems, Translated from the Russian by A. Parnakh (MIR Publishers, Moscow, 1978)

    Google Scholar 

  4. V.I. Utkin, J. Gulnder, J. Shi, Sliding Mode Control in Electromechanical Systems (CRC Press, Taylor and Francis Group, 1999)

    Google Scholar 

  5. C. Edwards, S.K. Spurgeon, Sliding Mode Control: Theory and Applications (CRC Press, Taylor and Francis Group, 1998)

    Google Scholar 

  6. H.S. Ramirez, Differential geometric methods in variable-structure control. Int. J. Control 48(4), 1359–1390 (1988)

    Google Scholar 

  7. J.-J. Slotine, S.S. Sastry, Tracking control of nonlinear systems using sliding surfaces with application to robot manipulator. Int. J. Control 38(2), 465–492 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  8. J.-J. Slotine, Sliding controller design for non-linear systems. Int. J. Control 40(2), 421–434 (1984)

    Article  MATH  Google Scholar 

  9. A.K. Behera, B. Bandyopadhyay, Event based robust stabilization of linear systems, in Proceedings of 40th Annual Conference of the IEEE Industrial Electronics Society, Dallas, USA (2014), pp. 133–138

    Google Scholar 

  10. A. Ferrara, G.P. Incremona, L. Magini, Model-Based Event-Triggered Robust MPC/ISM, in Proceedings of the 13th European Control Conference, Strausbourg, France (2014), pp. 2931–2936

    Google Scholar 

  11. A.K. Behera, B. Bandyopadhyay, Event based sliding mode control with quantized measurement, in Proceedings of International Workshop on Recent Advances Sliding Modes, Istanbul, Turkey (2015), pp. 1–6

    Google Scholar 

  12. A.K. Behera, B. Bandyopadhyay, Event-triggered sliding mode control for a class of nonlinear systems. Int. J. Control 89(9), 1916–1931 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. A.K. Behera, B. Bandyopadhyay, Robust sliding mode control: an event-triggering approach. IEEE Trans. Circuits Syst. II Express Briefs 64(2), 146–150 (2017)

    Article  Google Scholar 

  14. K.-E. Årźen, A simple event-based PID controller, in Proceedings of the 14th IFAC World Congrress, Beijing, China (1999), pp. 423–428

    Google Scholar 

  15. K.J. Åström, B. Bernhardsson, Comparison of Riemann and Lebesgue sampling for first order stochastic systems, in Proceedings of 41st IEEE Conference on Decision and Control, Las Vegas, USA (2002), pp. 2011–2016

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  17. Y.-K. Xu, X.-R. Cao, Lebesgue-sampling-based optimal control problems with time aggregation. IEEE Trans. Autom. Control 56(5), 1097–1109 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. W.P.M.H. Heemels, K.H. Johansson, P. Tabuada, An introduction to event-triggered and self-triggered control, in Proceedings of 51st IEEE Conference of Decision and Control, Hawai, USA (2010), pp. 3270–3285

    Google Scholar 

  19. P. Tabuada, X. Wang, Preliminary results on state-triggered stabilizing control tasks, in Proceedings of 45th IEEE Conference on Decision and Control, San Deigo, USA (2006), pp. 282–287

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bijnan Bandyopadhyay .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bandyopadhyay, B., Behera, A.K. (2018). Event-Triggered Sliding Mode Control for Nonlinear Systems. In: Event-Triggered Sliding Mode Control. Studies in Systems, Decision and Control, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-319-74219-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-74219-9_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74218-2

  • Online ISBN: 978-3-319-74219-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics