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Fuzzy Adaptive Sliding-Mode Control Scheme for Uncertain Underactuated Systems

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Advances and Applications in Nonlinear Control Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 635))

Abstract

This chapter proposes a fuzzy approximation-based adaptive sliding-mode control scheme for uncertain nonlinear perturbed underactuated systems. The underactuated system under study can be modeled by two subsystems. In the controller design, a sliding surface for each subsystem is defined and adaptive fuzzy systems are utilized to online estimate the unknown nonlinear functions. To estimate the fuzzy system parameters, a set of adaptation laws are appropriately designed. The boundedness of all signals of the closed-loop system as well as the asymptotic convergence of the underlying tracking errors to the origin are established based on a Lyapunov analysis. The main contributions of this chapter with respect to the existing works lie in the following: (1) The controller designed is free of model. (2) The stability analysis of the corresponding closed-loop system is rigorously proven by using some mild assumptions. (3) The uncertain interconnected terms are eliminated by appropriately designing a novel dynamic robust compensator. The effectiveness and robustness of the proposed adaptive fuzzy adaptive controller is illustrated through two simulation case studies taken from the underactuated system control literature.

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References

  1. Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, vol 576. Springer, Germany

    Google Scholar 

  2. Azar AT, Vaidyanathan S (2015) Handbook of research on advanced intelligent control engineering and automation. IGI Global, USA

    Book  Google Scholar 

  3. Boulkroune A, M’saad M (2011) A fuzzy adaptive variable-structure control scheme for uncertain chaotic MIMO systems with sector nonlinearities and dead-zones. Expert Syst Appl 38:4744–4750

    Article  Google Scholar 

  4. Boulkroune A, M’saad M (2012) On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign. Fuzzy Sets and Syst 201:71–85

    Article  MathSciNet  MATH  Google Scholar 

  5. Boulkroune A, M’saad M (2012) Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity. J Vib Control 18:437–450

    Article  MathSciNet  MATH  Google Scholar 

  6. Boulkroune A, M’saad M, Farza M (2012) Adaptive fuzzy tracking control for a class of MIMO nonaffine uncertain systems. Neurocomptiung 93:48–55

    Article  Google Scholar 

  7. Boulkroune A, M’saad M, Farza M (2012) Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction. IET Control Theory Appl 17:2619–2629

    Article  MathSciNet  Google Scholar 

  8. Boulkroune A, M’saad M, Farza M (2014) State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities. Int J Adv Manuf Technol 71:539–556

    Article  Google Scholar 

  9. Boulkroune A, Bounar N, M’saad M, Farza M (2014) Indirect adaptive fuzzy control scheme based on observer for nonlinear systems: a novel SPR-filter approach. Neurocomputing 135:378–387

    Article  Google Scholar 

  10. Boulkroune A, Tadjine M, M’saad M, Farza M (2008) How to design a fuzzy adaptive control based on observers for uncertain affine nonlinear systems. Fuzzy Sets Syst 159:926–948

    Article  MathSciNet  MATH  Google Scholar 

  11. Boulkroune A, Tadjine M, M’Saad M, Farza M (2014) Design of a unified adaptive fuzzy observer for uncertain nonlinear systems. Inf Sci 265:139–153

    Google Scholar 

  12. Boulkroune A, Bouzeriba A, Hamel S, Bouden T (2014) A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems. Nonlinear Dyn 78(1):433–447

    Article  MathSciNet  MATH  Google Scholar 

  13. Chaing C, Yeh Y (2014) Hierarchical fuzzy sliding mode control for uncertain nonlinear underactuated systems. In: Proceedings of the international conference on fuzzy systems (FUZZ-IEEE). Beijing, China, pp 662–669

    Google Scholar 

  14. Fang Y, Ma B, Wang P, Zhang X (2012) A motion planning-based adaptive control method for an under-actuated crane system. IEEE Trans Autom Control 20(1):241–248

    Google Scholar 

  15. Hao Y, Yi J, Zhao D, Qian D (2008) Robust control using incremental sliding mode for under-actuated systems with mismatched uncertainties. In: Proceedings of the American control conference. Seattle, Washington, USA, pp 532–537

    Google Scholar 

  16. Huang A-C, Chen Y-F (2010) Adaptive control for a class of underactuated system with mismatched uncertainties. In: Proceedings of the IEEE Chinese control conference. Beijing, China, pp 2053–2059

    Google Scholar 

  17. Huang J, Ding F, Wang Y (2013) Sliding mode control with nonlinear disturbance observer class of underactuated system. In: Proceedings of the Chinese control conference. Xi’an, China, pp 541–546

    Google Scholar 

  18. Hussein II, Bloch M (2008) Optimal control of underactuated nonholonomic mechanical systems. IEEE Trans Autom Control 53(3):668–682

    Article  MathSciNet  Google Scholar 

  19. Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice Hall, New Jersey

    Google Scholar 

  20. Kung CC, Chen T-H, Huang LC (2009) Adaptive fuzzy sliding mode control for a class under-actuated systems. In: Proceedings of the FUZZ-IEEE Conference. Korea, pp 1791–1795

    Google Scholar 

  21. Ming Y, Baoyin L (2012) Disturbance adaptive control for an under-actuated spherical robot based on hierarchical sliding-mode technology. In: Proceedings of the Chinese control conference. Hefei, China, pp 4787–4791

    Google Scholar 

  22. Nafa F, Labiod S, Chekireb H (2013) Direct adaptive fuzzy sliding mode decoupling control for a class of underactuated mechanical systems. Turk J Electr Eng Comput Sci 21(6):1615–1630

    Article  Google Scholar 

  23. Pezeshki S, Badamchizadeh MA, Ghiasi MA, Ghaemi S (2014) Control of overhead crane system Using adaptive model-free and adaptive fuzzy sliding mode controllers. J Control Autom Electr Syst 26:1–15

    Article  Google Scholar 

  24. Qian D, Yi J, Zhao D (2007) Hierarchical sliding mode control to swing up pendubot. In: Proceedings of the American control conference. New-York city, pp 5254–5258

    Google Scholar 

  25. Shine K, Yang Y, Cheng C (2012) Robust adaptive controller design for second-order under-actuated mechanical systems. In: Proceedings of the international conference in electric, communication and automatic control, pp 711–719

    Google Scholar 

  26. Slotine JJE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  27. Tuan L, Lee S (2013) Sliding mode controls of double-pendulum crane systems. J Mech Sci Technol 23(10):1863–1873

    Article  Google Scholar 

  28. Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  29. Wang W, Zhao J, Liu D (2004) Design of a stable sliding-mode controller for class of second-order under-actuated systems. IEE Proc Control Theory Appl 151(6):683–690

    Article  MathSciNet  Google Scholar 

  30. Yue M, Liu B (2014) Adaptive control of an under-actuated spherical robot with a dynamic stable equilibrium point using hierarchical sliding mode approach. Int J Adapt Control Signal Process 28(6):523–535

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LAJ, University of Jijel, BP. 98, Ouled-Aissa, 18000, Jijel, Algeria

    Soumia Moussaoui & Abdesselem Boulkroune

  2. R & D Centre, Vel Tech University, Chennai, India

    Sundarapandian Vaidyanathan

Authors
  1. Soumia Moussaoui
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  2. Abdesselem Boulkroune
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  3. Sundarapandian Vaidyanathan
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Corresponding author

Correspondence to Abdesselem Boulkroune .

Editor information

Editors and Affiliations

  1. Chennai, India

    Sundarapandian Vaidyanathan

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

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Moussaoui, S., Boulkroune, A., Vaidyanathan, S. (2016). Fuzzy Adaptive Sliding-Mode Control Scheme for Uncertain Underactuated Systems. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Nonlinear Control Systems. Studies in Computational Intelligence, vol 635. Springer, Cham. https://doi.org/10.1007/978-3-319-30169-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-30169-3_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30167-9

  • Online ISBN: 978-3-319-30169-3

  • eBook Packages: EngineeringEngineering (R0)

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