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Adaptive Fuzzy Sliding Mode Control for a Class of Uncertain Nonaffine Nonlinear Strict-Feedback Systems

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Abstract

In this paper, an adaptive fuzzy sliding mode scheme is proposed for a class of single-input, single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. In this scheme, the backstepping algorithm is used to obtain the virtual controllers. The real control law is designed by using sliding mode approach. The both matched and mismatched unknown uncertainties are counteracted by using adaptive robust terms. The unknown nonlinear functions are approximated by employing adaptive fuzzy logic systems. The adaptation laws of the adjustable parameters are deduced from the stability analysis of the closed-loop system in the sense of Lyapunov. The derived adaptive fuzzy sliding mode control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a very small neighborhood of the origin. Numerical simulation results are provided to show the effectiveness of the proposed control scheme.

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References

  • Boskovic JD, Chen LJ, Mehra RK (2001) Multivariable adaptive controller design for a class of non-affine models arising in flight control. In: Proceedings of the 40th IEEE conference on decision and control, Orlando, Florida, USA, pp 2442–2447

  • Chen B, Liu X, Liu K, Lin C (2009) Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6):1530–1535

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TS, Ming LY (2010) Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci China Inf Sci 53(2):307–324

    Article  MathSciNet  Google Scholar 

  • Cui Y, Zhang H, Wang Y, Gao W (2016) Adaptive control for a class of uncertain strict-feedback nonlinear systems based on a generalized fuzzy hyperbolic model. Fuzzy Sets Syst 302:52–64

    Article  MathSciNet  MATH  Google Scholar 

  • Doudou S, Khaber F (2012) Direct adaptive fuzzy control of a class of MIMO non-affine nonlinear systems. Int J Syst Sci 43(6):1029–1038

    Article  MathSciNet  MATH  Google Scholar 

  • Doudou S, Khaber F, Bouden T (2014) Direct adaptive fuzzy control of a class of MIMO nonaffine nonlinear systems using gradient descent method. In: Proceeding of the first international conference on technological advances in electrical engineering, ICTAEE’14, Skikda-Algeria

  • Drakunov S, Utkin V (1992) Sliding mode control in dynamic systems. Int J Control 55(4):1029–1037

    Article  MathSciNet  MATH  Google Scholar 

  • Ge SS, Hang CC, Zhang T (1999) Nonlinear adaptive control using neural networks and its application to CSTR systems. J Process Control 9(4):313–323

    Article  Google Scholar 

  • Ho HF, Wong YK, Rad AB (2008) Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form. ISA Trans 47(3):286–299

    Article  Google Scholar 

  • Hou Z, Jin S (2011) A novel data-driven control approach for a class of discrete-time nonlinear systems. IEEE Trans Control Syst Technol 19(6):1549–1558

    Article  Google Scholar 

  • Isidori A (1989) Nonlinear control systems. Springer, Berlin

    Book  MATH  Google Scholar 

  • Kanellakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control 36(11):1241–1253

    Article  MathSciNet  MATH  Google Scholar 

  • Khaber F, Hamzaoui A, Zehar K, Essounbouli N (2006) New stable adaptive fuzzy approach to control uncertain nonlinear SISO systems. Int J Syst Sci 37(7):437–445

    Article  MATH  Google Scholar 

  • Krstic M, Kanellakopoulos L, Kokotovic PV (1995) Nonlinear and adaptive control design. Wiley, New York

    MATH  Google Scholar 

  • Labiod S, Guerra TM (2017) Adaptive fuzzy control for a class of multivariable nonlinear systems with unknown control direction. IFAC Papers OnLine 50(1):2995–3000

    Article  Google Scholar 

  • Lui YJ, Tong S, Li Y (2008) Adaptive robust fuzzy control for a class of nonlinear systems based on backstepping method. In: Proceeding of Chinese control and decision conference, Yantai, China, pp 3403–3408

  • Polycarpouddd MM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Autom Control 41(3):447–451

    Article  MathSciNet  Google Scholar 

  • Qiu J, Tian H, Lu Q, Gao H (2013) Non-synchronized robust filtering design for continuous-time T–S fuzzy affine dynamic systems based on piecewise Lyapunov functions. IEEE Trans Cybern 43(6):1755–1766

    Article  Google Scholar 

  • Qiu J, Wang T, Yin S, Gao H (2017a) Data-based optimal control for networked double-layer industrial processes. IEEE Trans Ind Electron 64(5):4179–4186

    Article  Google Scholar 

  • Qiu J, Wei Y, Wu L (2017b) A novel approach to reliable control of piecewise affine systems with actuator faults. IEEE Trans Circuits Syst II Express Briefs 64(8):957–961

    Article  Google Scholar 

  • Qiu J, Wei Y, Karim HR, Gao H (2018) Reliable control of discrete-time piecewise-affine time-delay systems via output feedback. IEEE Trans Reliab 67(1):79–91

    Article  Google Scholar 

  • Ren C, Tong S, Li Y (2012) Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties. Nonlinear Dyn 67(2):941–955

    Article  MathSciNet  MATH  Google Scholar 

  • Seto D, Annaswamy AM, Baillieul J (1994) Adaptive control of nonlinear systems with a triangular structure. IEEE Trans Autom Control 39(7):1411–1428

    Article  MathSciNet  MATH  Google Scholar 

  • Shiriaev AS, Ludvigsen H, Egeland O, Fradkov AL (1999) Swinging up of nonaffine in control pendulum. In: Proceedings of the American control conference, San Diego, California, USA, pp 4039–4044

  • Slotine JJ (1984) Sliding controller design for nonlinear systems. Int J Control 40(2):421–434

    Article  MathSciNet  MATH  Google Scholar 

  • Slotine JJ (1987) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Slotine JJ, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  • Tong SC (2006) Indirect adaptive fuzzy backstepping control for nonlinear systems. In: Proceedings of the 5th international conference on machine learning and cybernetics, Dalian, pp 468–473

  • Utkin V (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control 22(2):212–222

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Wang M, Chen B, Dai SL (2007) Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems. Fuzzy Sets Syst 158(24):2655–2670

    Article  MathSciNet  MATH  Google Scholar 

  • Wang M, Xiuying W, Chen B, Tong S (2007a) Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique. J Control Theory Appl 5(3):317–322

    Article  MathSciNet  Google Scholar 

  • Wang WY, Li IH, Chien LC, Su SF (2007b) On-line modeling and control via T–S fuzzy models for nonaffine nonlinear systems using a second type adaptive fuzzy approach. Int J Fuzzy Syst 9(4):152–161

    MathSciNet  Google Scholar 

  • Wang F, Liu Z, Zhang Y, Chen X, Chen CLP (2015) Adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone and dynamic uncertainties. Nonlinear Dyn 79(3):1693–1709

    Article  MATH  Google Scholar 

  • Wang T, Zhang Y, Qiu J, Gao H (2015) Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements. IEEE Trans Fuzzy Syst 23(2):302–312

    Article  Google Scholar 

  • Wang T, Qiu J, Yin S, Gao H, Fan J, Chai T (2016) Performance-based adaptive fuzzy tracking control for networked industrial processes. IEEE Trans Cybern 46(8):1760–1770

    Article  Google Scholar 

  • Wang T, Qiu J, Fu S, Ji W (2017a) Distributed fuzzy H-infinity filtering for nonlinear multirate networked double-layer industrial processes. IEEE Trans Ind Electron 64(6):5203–5211

    Article  Google Scholar 

  • Wang T, Qiu J, Gao H, Wang C (2017b) Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy. IEEE Trans Syst Man Cybern Syst 47(8):2137–2147

    Article  Google Scholar 

  • Wen J (2011) Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear system. In: Proceeding of the 9th IEEE international conference on control and automation, Santiago, Chile, pp 1255–1260

  • Wen J, Jiang C (2011) Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear systems. J Syst Eng Electron 22(6):967–974

    Article  Google Scholar 

  • Zhang X, Liu X, Li Y (2017) Adaptive fuzzy tracking control for nonlinear strict-feedback systems with unmodeled dynamics via backstepping technique. Neurocomputing 235:182–191

    Article  Google Scholar 

  • Zhao QC, Ji W (2012) Adaptive fuzzy control for a class of non-linear systems. IMA J Math Control Inf 29(4):573–592

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou S, Feng G, Feng CB (2005) Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping. Fuzzy Sets Syst 151(1):1–20

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou WD, Liao CY, Zheng L, Liu MM (2015) Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input. Nonlinear Dyn 79(4):2609–2621

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. QUERE Laboratory, University of Setif 1, 19000, Sétif, Algeria

    Sofiane Doudou & Farid Khaber

  2. Department of Automatic, University of Jijel, 18000, Jijel, Algeria

    Sofiane Doudou

Authors
  1. Sofiane Doudou
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  2. Farid Khaber
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Correspondence to Sofiane Doudou.

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Doudou, S., Khaber, F. Adaptive Fuzzy Sliding Mode Control for a Class of Uncertain Nonaffine Nonlinear Strict-Feedback Systems. Iran J Sci Technol Trans Electr Eng 43, 33–45 (2019). https://doi.org/10.1007/s40998-018-0144-7

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  • DOI: https://doi.org/10.1007/s40998-018-0144-7

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