Skip to main content
SpringerLink
Log in

On Fixed-Time Convergent Sliding Mode Control Design and Applications

  • Chapter
  • First Online:
Emerging Trends in Sliding Mode Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 318))

  • 651 Accesses

Abstract

This chapter discusses an algorithm to provide arbitrary-order fixed-time convergent SMC design. Through numerical simulation and comparative study, it is shown that in the proposed algorithm, the convergence speed does not depend on the initial condition. Moreover, it is also evident from the simulations that a higher control effort will be required by achieving so and is discussed thoroughly in the chapter, leading to a trade-off between the control effort and convergence speed. Subsequently, a novel distributed algorithm is developed for achieving second-order consensus in the multi-agent systems by designing a full-order fixed-time convergent sliding surface as an application to the proposed algorithm with suitable numerical simulations.

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

Access this chapter

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 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
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. Utkin, V.: Discussion aspects of high-order sliding mode control. IEEE Trans. Autom. Control 61(3), 829–833 (2016)

    Article  MathSciNet  Google Scholar 

  2. Yu, S., Long, X.: Finite-time consensus tracking of perturbed high-order agents with relative information by integral sliding mode. IEEE Trans. Circuits Syst. II Express Briefs 63(6), 563–567 (2016)

    Article  Google Scholar 

  3. Tan, S.-C., Lai, Y.-M., Tse, C.K.: A unified approach to the design of PWM-based sliding-mode voltage controllers for basic DC-DC converters in continuous conduction mode. IEEE Trans. Circuits Syst. I Regul. Pap. 53(8), 1816–1827 (2006)

    Article  Google Scholar 

  4. Levant, A.: Chattering analysis. IEEE Trans. Autom. Control 55(6), 1380–1389 (2010)

    Article  MathSciNet  Google Scholar 

  5. Moreno, J.A., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control 57(4), 1035–1040 (2012)

    Article  MathSciNet  Google Scholar 

  6. Ding, S., Levant, A., Li, S.: Simple homogeneous sliding-mode controller. Automatica 67, 22–32 (2016)

    Article  MathSciNet  Google Scholar 

  7. Cruz-Zavala, E., Moreno, J.A.: Homogeneous high order sliding mode design: a Lyapunov approach. Automatica 80, 232–238 (2017)

    Article  MathSciNet  Google Scholar 

  8. Kamal, S., Chalanga, A., Moreno, J., Fridman, L., Bandyopadhyay, B.: Higher order super-twisting algorithm. In: 13th International Workshop on Variable Structure Systems (VSS). IEEE, pp 1–5 (2014)

    Google Scholar 

  9. Mishra, J., Yu, X., Jalili, M.: Arbitrary-order continuous finite-time sliding mode controller for fixed-time convergence. IEEE Trans. Circuits Syst. II Express Briefs 65(12), 1988–1992 (2018)

    Article  Google Scholar 

  10. Mishra, J.P., Yu, X., Jalili, M.: A new class of generalized continuous robust control algorithm for arbitrary order systems. In: Australian Control Conference (AuCC). IEEE, pp 77–80 (2016)

    Google Scholar 

  11. Kamal, S., Ramesh Kumar, P., Chalanga, A., Goyal, J.K., Bandyopadhyay, B., Fridman, L.: A new class of uniform continuous higher-order sliding mode controllers. J. Dyn. Syst. Meas. Control. 142(1) (2020)

    Google Scholar 

  12. Basin, M.V., Yu, P., Shtessel, Y.B.: Hypersonic missile adaptive sliding mode control using finite-and fixed-time observers. IEEE Trans. Indus. Electron. 65(1), 930–941 (2018)

    Article  Google Scholar 

  13. Yu, X., Man, Z.: Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49(2), 261–264 (2002)

    Article  MathSciNet  Google Scholar 

  14. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

    Article  MathSciNet  Google Scholar 

  15. Polyakov, A., Efimov, D., Perruquetti, W.: Finite-time and fixed-time stabilization: implicit Lyapunov function approach. Automatica 51, 332–340 (2015)

    Article  MathSciNet  Google Scholar 

  16. Ríos, H., Efimov, D., Moreno, J.A., Perruquetti, W., Rueda-Escobedo, J.G.: Time-varying parameter identification algorithms: finite and fixed-time convergence. IEEE Trans. Autom. Control 62(7), 3671–3678 (2017)

    Article  MathSciNet  Google Scholar 

  17. Feng, Y., Han, F., Yu, X.: Chattering free full-order sliding-mode control. Automatica 50(4), 1310–1314 (2014)

    Article  MathSciNet  Google Scholar 

  18. Slotine, J.-J.E., Li, W., et al.: Applied Nonlinear Control, vol. 199, no. 1. Prentice Hall Englewood Cliffs, NJ, USA (1991)

    Google Scholar 

  19. Abramowitz, M., Stegun, I.A., et al.: Handbook of mathematical functions. Appl. Math. Ser. 55, 62 (1966)

    Google Scholar 

  20. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18. Springer Science & Business Media, NY, USA (2013)

    Google Scholar 

  21. Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control. Signals Syst. (MCSS) 17(2), 101–127 (2005)

    Google Scholar 

  22. Basin, M., Panathula, C.B., Shtessel, Y.: Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control. Int. J. Control 89(9), 1777–1787 (2016)

    Article  MathSciNet  Google Scholar 

  23. Basin, M., Shtessel, Y., Aldukali, F.: Continuous finite-and fixed-time high-order regulators. J. Frankl. Inst. 353(18), 5001–5012 (2016)

    Article  MathSciNet  Google Scholar 

  24. Liu, X., Chen, T.: Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans. Autom. Control 60(12), 3316–3321 (2015)

    Article  MathSciNet  Google Scholar 

  25. Mishra, J.P., Li, C., Jalili, M., Yu, X.: Robust second-order consensus using a fixed-time convergent sliding surface in multiagent systems. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2018.2875362

  26. Barabási, A.-L., Frangos, J.: Linked: the new science of networks science of networks. Basic Books, NY, USA (2002)

    Google Scholar 

  27. Albert, R., Jeong, H., Barabási, A.-L.: Internet: diameter of the world-wide web. Nature 401(6749), 130 (1999)

    Article  Google Scholar 

  28. Barabasi, A.-L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5(2), 101 (2004)

    Article  Google Scholar 

  29. Barabási, A.-L., Gulbahce, N., Loscalzo, J.: Network medicine: a network-based approach to human disease. Nat. Rev. Genet. 12(1), 56 (2011)

    Article  Google Scholar 

  30. Andrieu, V., Praly, L., Astolfi, A.: Homogeneous approximation, recursive observer design, and output feedback. SIAM J. Control. Optim. 47(4), 1814–1850 (2008)

    Article  MathSciNet  Google Scholar 

  31. Gross, J.L., Yellen, J.: Handbook of Graph Theory. CRC Press, NY, USA (2004)

    MATH  Google Scholar 

  32. Yu, W., Wang, H., Cheng, F., Yu, X., Wen, G.: Second-order consensus in multiagent systems via distributed sliding mode control. IEEE Trans. Cybern. 47(8), 1872–1881 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering, RMIT University, Melbourne, 3000, Australia

    Jyoti Mishra & Xinghuo Yu

Authors
  1. Jyoti Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinghuo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jyoti Mishra .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Institute of Infrastructure, Technology, Research and Management, Ahmedabad, Gujarat, India

    Axaykumar Mehta

  2. Interdisciplinary Programme in Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Bijnan Bandyopadhyay

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mishra, J., Yu, X. (2021). On Fixed-Time Convergent Sliding Mode Control Design and Applications. In: Mehta, A., Bandyopadhyay, B. (eds) Emerging Trends in Sliding Mode Control. Studies in Systems, Decision and Control, vol 318. Springer, Singapore. https://doi.org/10.1007/978-981-15-8613-2_9

Download citation

Publish with us

Policies and ethics

Search

Navigation