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Adaptive Fuzzy Control for Stochastic Nonlinear Systems via Sliding Mode Method

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Abstract

In this paper, an adaptive fuzzy controller is designed for a nonlinear stochastic system to track the given reference via the sliding mode method. The nonlinear stochastic system is modeled by a deterministic nonlinear system with white noise obtained from the derivative of a Wiener process, which eventually generates an Itô differential equation. Compared with existing results, the main advantage is that information of the nonlinear functions is not required. Under the designed controller with the proposed update laws, the tracking error trajectories converge to an arbitrary small region around zero in the mean square norm. Simulations to show the efficiency of the proposed controller are provided.

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References

  1. P. Balasubramaniam, M. Kalpana, R. Rakkiyappan, Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst. Signal Process. 30, 1595–1616 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Feng, S.Q. Wang, Reliable fuzzy control for a class of nonlinear networked control systems with time delay. Acta Autom. Sin. 38(7), 1091–1099 (2012)

    MATH  Google Scholar 

  3. H.K. Khail, Adaptive output feedback control of nonlinear systems represented by input-output models. IEEE Trans. Autom. Control 41, 177–188 (1996)

    Article  Google Scholar 

  4. R.Z. Khasminskii, Stochastic Stability of Differential Equations (Sijthoff and Noordhoff, Amsterdam, 1980)

    Book  Google Scholar 

  5. C. Kyrtsou, M. Terraza, Stochastic chaos or ARCH effects in stock series? A comparative study. Int. Rev. Financ. Anal. 11, 407–431 (2002)

    Article  Google Scholar 

  6. S. Labiod, Comments on ‘Fuzzy adaptive sliding-mode control for MIMO nonlinear systems’. IEEE Trans. Fuzzy Syst. 14(3), 478–482 (2006)

    Article  Google Scholar 

  7. S. Labiod, M.S. Boucherit, T.M. Guerra, Adaptive fuzzy control of a class of MIMO nonlinear systems. Fuzzy Sets Syst. 151, 59–77 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. Li, Y.M. Li, S.C. Tong, Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large-scale systems. Neurocomputing 83, 38–46 (2012)

    Article  Google Scholar 

  9. J. Lian, F. Zhang, P. Shi, Sliding mode control of uncertain stochastic hybrid delay systems with average dwell time. Circuits Syst. Signal Process. 31, 539–553 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. S.L. Liu, Z.R. Xiang, Exponential H ∞ output tracking control for switched neutral system with time-varying delay and nonlinear perturbations. Circuits Syst. Signal Process. 32, 103–121 (2013)

    Article  MathSciNet  Google Scholar 

  11. X.Y. Lu, S.K. Spurgeon, Robust sliding mode control of uncertain nonlinear systems. Syst. Control Lett. 32, 75–90 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Muralisankar, N. Gopalakrishnan, P. Balasubramaniam, Robust exponential stability criteria for TCS fuzzy stochastic delayed neural networks of neutral type. Circuits Syst. Signal Process. 30, 1617–1641 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. B. Oksendal, Stochastic differential equations, in An Introduction with Applications (Springer, Berlin, 1992)

    Google Scholar 

  14. P.R. Patnaik, The extended Kalman filter as a noise modulator for continuous yeast cultures under monotonic, oscillating and chaotic conditions. Chem. Eng. J. 108, 1–9 (2005)

    Article  Google Scholar 

  15. H. Salarieh, A. Alasty, Adaptive control of chaotic systems with stochastic time varying unknown parameters. Chaos Solitons Fractals 38, 168–177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Salarieh, A. Alasty, Chaos synchronization of nonlinear gyros in presence of stochastic excitation via sliding mode control. J. Sound Vib. 313, 760–771 (2008)

    Article  Google Scholar 

  17. H. Salarieh, A. Alasty, Adaptive chaos synchronization in Chua’s systems with noisy parameters. Math. Comput. Simul. 79, 233–241 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. H. Salarieh, A. Alasty, Control of stochastic chaos using sliding mode method. J. Comput. Appl. Math. 225, 135–145 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. T. Senthilkumar, P. Balasubramaniam, Robust H ∞ control for nonlinear uncertain stochastic TCS fuzzy systems with time delays. Appl. Math. Lett. 24, 1986–1994 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. P. Shi, Y. Xia, G.P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006)

    Article  MathSciNet  Google Scholar 

  21. S.C. Tong, H.X. Li, Fuzzy adaptive sliding-mode control for MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 11, 354–360 (2003)

    Article  Google Scholar 

  22. L.X. Wang, J.M. Mendel, Fuzzy basis function, universal approximation, and orthogonal least square learning. IEEE Trans. Neural Netw. 3, 807–814 (1992)

    Article  Google Scholar 

  23. T. Wang, S.C. Tong, Y.M. Li, Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction. Neurocomputing (2012). doi:10.1016/j.neucom.2012.10.013

    Google Scholar 

  24. T. Wang, S.C. Tong, Y.M. Li, Robust adaptive decentralized fuzzy control for stochastic large-scale nonlinear systems with dynamical uncertainties. Neurocomputing 97, 33–43 (2012)

    Article  Google Scholar 

  25. H.Q. Wang, B. Chen, C. Li, Adaptive fuzzy decentralized control for a class of large-scale stochastic nonlinear systems. Neurocomputing 103, 155–163 (2013)

    Article  Google Scholar 

  26. C. Wu, Y. Lei, T. Fang, Stochastic chaos in a Duffing oscillator and its control. Chaos Solitons Fractals 27, 459–469 (2005)

    Article  MathSciNet  Google Scholar 

  27. H.B. Zhang, G. Feng, C.Y. Dang, An approach to H ∞ control of a class of nonlinear stochastic systems. Circuits Syst. Signal Process. 31, 127–141 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the reviewers for their valuable comments and suggested corrections which have greatly helped us in improving the quality of the paper. This work was supported by the National Natural Science Foundation of China (11071060), Special Funds of the National Natural Science Foundation of China (11226143), the Natural Science Foundation of Hunan Province (13JJ4111), the scientific Research Fund of the Hunan Provincial Education Department (11B029, 10C0524), and the science Foundation of Hunan First Normal University (XYS11N03).

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Authors and Affiliations

  1. Department of Mathematics, Hunan First Normal University, Changsha, 410205, Hunan, China

    Zengyun Wang & Xuxin Yang

  2. College of Mathematics and Economtrics, Hunan University, Changsha, 410082, Hunan, China

    Lihong Huang

  3. Hunan Women’s University, Changsha, 410003, Hunan, China

    Lihong Huang

  4. Department of Information Science and Engineering, Hunan First Normal University, Changsha, 410205, Hunan, China

    Aitong Xin

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  1. Zengyun Wang
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  2. Lihong Huang
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  3. Xuxin Yang
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Correspondence to Zengyun Wang.

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Wang, Z., Huang, L., Yang, X. et al. Adaptive Fuzzy Control for Stochastic Nonlinear Systems via Sliding Mode Method. Circuits Syst Signal Process 32, 2839–2850 (2013). https://doi.org/10.1007/s00034-013-9602-7

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  • DOI: https://doi.org/10.1007/s00034-013-9602-7

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