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Design of neural network based sliding mode controller for a class of nonlinear system: an event-triggered framework

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Abstract

This paper investigates the design of robust event-triggered neuro sliding mode controller for a class of single input single output uncertain nonlinear system whose nonlinearities are unknown. In this work, the radial basis function neural network is used to approximate these nonlinearities of the system with an adaptive weight update law. The sliding mode controller is designed with these approximated system dynamics where the traditional periodic sampling and update of control law is avoided. This neuro sliding mode controller (NSMC) is designed with a nonuniform sampling approach called event-based sampling. This control strategy not only relaxes the knowledge of complete system dynamics to implement the control law, guarantees the robustness and at the same time it reduces the computation burden and communication bandwidth without compromising the system stability. A numerical example of nonlinear system is simulated with the proposed event-triggered NSMC to evaluate its performance.

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References

  1. Gupta RA, Chow M (2010) Networked control system: overview and research trends. IEEE Trans Industr Electron 57(7):2527–2535

    Article  Google Scholar 

  2. Zhang D, Shi P, Wang QG, Yu L (2017) Analysis and synthesis of networked control systems: a survey of recent advances and challenges. ISA Trans 66:376–392

    Article  Google Scholar 

  3. Wang FY, Liu D (2008) Networked control systems: theory and applications. Springer, London

    Book  Google Scholar 

  4. Donkers MC, Tabuada P, Heemels WP (2014) Minimum attention control for linear systems. Discrete Event Dyn Syst 24(2):199–218

    Article  MathSciNet  Google Scholar 

  5. Heemels WPMH, Johansson KH, Tabuada P (2012) An introduction to event-triggered and self-triggered control. In: 2012 IEEE 51st IEEE conference on decision and control (CDC), pp 3270–3285

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

    Article  MathSciNet  Google Scholar 

  7. Åarzén KE (1999) A simple event-based PID controller. In: IFAC proceedings volumes 32, no. 2, pp 8687–8692, 14th IFAC World Congress 1999, Beijing, Chia, 5–9 July

  8. Heemels WPMH, Sandee JH, Bosch PPJVD (2008) Analysis of event-driven controllers for linear systems. Int J Control 81(4):571–590

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Abdelrahim M, Postoyan R, Daafouz J, Nešić D (2014) Co-design of output feedback laws and event-triggering conditions for linear systems. In: 53rd IEEE conference on decision and control, pp 3560–3565

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

    Article  Google Scholar 

  12. Tallapragada P, Chopra N (2013) On event triggered tracking for nonlinear systems. IEEE Trans Autom Control 58(9):2343–2348

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Azimi MM, Afzalian AA, Ghaderi R (2020) Decentralized stabilization of a class of large scale networked control systems based on modified event-triggered scheme. Int J Dyn Control, pp 1–11

  15. Hassani H, Mansouri A, Ahaitouf A (2020) Robust autonomous flight for quadrotor UAV based on adaptive nonsingular fast terminal sliding mode control. Int J Dyn Control, pp 1–17

  16. Bandyopadhyay B, Behera AK (2018) Event-triggered sliding mode control a new approach to control system design. Springer, Berlin

    Book  Google Scholar 

  17. Yesmin A, Bera MK (2020) Design of event-based sliding mode controller with logarithmic quantized state measurement and delayed control update. In: ISA transactions

  18. Yesmin A, Bera MK (2020) Design of event-triggered integral sliding mode controller for systems with matched and unmatched uncertainty. In: Emerging trends in sliding mode control. Springer, pp 145–160

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

    Article  Google Scholar 

  20. Wen S, Huang T, Yu X, Chen MZQ, Zeng Z (2017) Sliding-mode control of memristive Chua’s systems via the event-based method. IEEE Trans Circuits Syst II Express Briefs 64(1):81–85

  21. Yesmin A, Bera MK (2019) Design of event-triggered sliding mode controller based on reaching law with time varying event generation approach. Eur J Control 48:30–41

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  23. Kumari K, Behera AK, Bandyopadhyay B (2018) Event-triggered sliding mode-based tracking control for uncertain Euler-Lagrange systems. IET Control Theory Appl 12(9):1228–1235

    Article  MathSciNet  Google Scholar 

  24. Cucuzzella M, Incremona GP, Ferrara A (2019) Event-triggered variable structure control. Int J Control, pp 1–9

  25. Mustafa A, Dhar NK, Verma NK (2020) Event-triggered sliding mode control for trajectory tracking of nonlinear systems. IEEE/CAA J Autom Sin 7(1):307–314

    Article  MathSciNet  Google Scholar 

  26. Kaynak O, Erbatur K, Ertugnrl M (2001) The fusion of computationally intelligent methodologies and sliding-mode control-a survey. IEEE Trans Industr Electron 48(1):4–17

    Article  Google Scholar 

  27. Yue M, Wang L, Ma T (2017) Neural network based terminal sliding mode control for WMRs affected by an augmented ground friction with slippage effect. IEEE/CAA J Autom Sin 4(3):498–506

    Article  MathSciNet  Google Scholar 

  28. Kumar N et al (2019) Finite time control scheme for robot manipulators using fast terminal sliding mode control and RBFNN. Int J Dyn Control 7(2):758–766

    Article  MathSciNet  Google Scholar 

  29. Le HX, Van Nguyen T, Le AV, Phan TA, Nguyen NH, Phan MX (2019) Adaptive hierarchical sliding mode control using neural network for uncertain 2D overhead crane. Int J Dyn Control 7(3):996–1004

    Article  MathSciNet  Google Scholar 

  30. Wang J, Liu Z, Zhang Y, Chen CP (2019) Neural adaptive event-triggered control for nonlinear uncertain stochastic systems with unknown hysteresis. IEEE Trans Neural Netw Learn Syst 30(11):3300–3312

    Article  MathSciNet  Google Scholar 

  31. Sahoo A, Xu H, Jagannathan S (2015) Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans Neural Netw Learn Syst 27(3):497–509

    Article  MathSciNet  Google Scholar 

  32. Isidori A (2001) Nonlinear systems. Springer, London

    MATH  Google Scholar 

  33. Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

    Article  Google Scholar 

  34. Barron AR (1993) Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans Inf Theory 39(3):930–945

    Article  MathSciNet  Google Scholar 

  35. Utkin VI (1992) Sliding modes in control and optimization. Springer, Berlin

    Book  Google Scholar 

  36. Filippov AF (1988) Differential equations with discontinuous right-hand sides. Springer, Dordrecht

    Book  Google Scholar 

  37. Ioannou P, Fidan B (2007) Adaptive control tutorial. Soc Ind Appl Math

  38. Khalil HK (1995) Nonlinear control systems. Prentice Hall, Hoboken

    Google Scholar 

  39. Cucuzzella M, Incremona GP, Ferrara A (2019) Event-triggered variable structure control. Int J Control, pp 1–9

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Authors and Affiliations

  1. Department of Electronics and Instrumentation Engineering, National Institute of Technology, Silchar, India

    Krishanu Nath & Manas Kumar Bera

Authors
  1. Krishanu Nath
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  2. Manas Kumar Bera
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Contributions

All authors contributed to the conceptualization and formal analysis of the manuscript. Original draft and Simulations were performed by Krishanu Nath. Supervision, review and editing of the final draft were performed by Manas Kumar Bera.

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Correspondence to Krishanu Nath.

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Nath, K., Bera, M.K. Design of neural network based sliding mode controller for a class of nonlinear system: an event-triggered framework. Int. J. Dynam. Control 10, 785–799 (2022). https://doi.org/10.1007/s40435-021-00864-7

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  • DOI: https://doi.org/10.1007/s40435-021-00864-7

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