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Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms

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Abstract

Adaptive control of a class of uncertain multi-input/multi-output (MIMO) non-linear systems in block-triangular forms is considered in this paper. By incorporating dynamic surface approach and “minimal learning parameters” algorithm, a systematic procedure for the synthesis of stable adaptive fuzzy tracking controllers with less tuning parameters is developed. Takagi–Sugeno (T-S) fuzzy logic systems (FLSs) are used to approximate those unstructured system functions rather than the unknown virtual control gain functions. Consequently, the potential controller singularity problem can be overcome. Moreover, both problems of “explosion of learning parameters” and “explosion of complexity” are avoided. The computational burden has thus been greatly reduced. The stability in the sense of semi-globally uniform ultimate boundedness (SGUUB) of the closed-loop MIMO systems is established via Lyapunov stability theorem. Finally, simulation results are presented to demonstrate the effectiveness and the advantages of the proposed control approach.

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References

  1. Chen, B., Liu, X.P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes. IEEE Trans. Fuzzy Syst. 13(6), 832–847 (2005)

    Article  Google Scholar 

  2. Chen, B., Tong, S.C., Liu, X.P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach. Fuzzy Sets Syst. 158, 1097–1125 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, B., Liu, X.P., Tong, S.C.: Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems. IEEE Trans. Fuzzy Syst. 15(2), 287–300 (2007)

    Article  Google Scholar 

  4. Chen, C.: Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems. Inform. Sci. 179, 2676–2688 (2009)

    Article  MATH  Google Scholar 

  5. Ge, S.S., Hang, C.C., Zhang, T.: Stable adaptive control for multivariable systems with a triangular control structure. IEEE Trans. Autom. Control 45, 1221–1225 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ge, S.S., Wang, C.: Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans. Neural Netw. 15(3), 674–692 (2004)

    Article  Google Scholar 

  7. Labiod, S., Boucherit, M.S., Guerra, T.M.: Adaptive fuzzy control of a class of MIMO nonlinear systems. Fuzzy Sets Syst. 151(1), 58–77 (2005)

    Article  MathSciNet  Google Scholar 

  8. Li, T.S., Feng, G., Zou, Z.J.: DSC-backstepping based robust adaptive fuzzy control for a class of strict-feedback nonlinear systems. In: Proc. WCCI08-FUZZ-IEEE 2008, pp. 1274–1281. Hong Kong, China, June 1–6, (2008)

  9. Liu, X., Zhang, H., Dai, J.: Delay-dependent robust and reliable H-infinite fuzzy hyperbolic decentralized control for a class of nonlinear large-scale systems. Int. J. Fuzzy Sets Syst. 161(6), 872–892 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inform. Sci. 177, 3901–3917 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Liu, Y.J., Wang, Z.F.: Adaptive fuzzy controller design of nonlinear systems with unknown gain sign. Nonlinear Dyn. 58(4), 687–695 (2009)

    Article  MATH  Google Scholar 

  12. Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)

    Google Scholar 

  14. Tong, S.C., Tang, J.T., Wang, T.: Fuzzy adaptive control of multivariable nonlinear systems. Fuzzy Sets Syst. 111(2), 153–167 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tong, S.C., Li, H.X.: Fuzzy adaptive sliding model control for MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 11(3), 354–360 (2003)

    Article  Google Scholar 

  16. Tong, S.C., Li, H.X., Chen, G.R.: Adaptive fuzzy control for decentralized control for a class of large-scale nonlinear systems. IEEE Trans. Syst., Man, Cybern. B: Cybern. 34(1), 770–775 (2004)

    Article  Google Scholar 

  17. Tong, S.C., Li, Y.M., Shi, P.: Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties. Inform. Sci. 179, 1319–1332 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Tseng, C.-S.: A novel approach to H ∞ decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems. IEEE Trans. Fuzzy Syst. 16(56), 1337–1350 (2008)

    Article  MathSciNet  Google Scholar 

  19. Wang, D., Huang, J.: Neural Network-Based Adaptive Dynamic Surface Control for a Class of Uncertain Nonlinear Systems in Strict-Feedback Form. IEEE Trans. Neural Netw. 16(1), 195–202 (2005)

    Article  Google Scholar 

  20. Wang, M., Chen, B., Liu, K.F., Liu, X.P., Zhang, S.Y.: Adaptive fuzzy tracking control of time-delay systems with unknown virtual control coefficients. Inform. Sci. 178, 4326–4340 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Yang, Y.S., Ren, J.S.: Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans. Fuzzy Syst. 11(6), 783–795 (2003)

    Article  Google Scholar 

  22. Yang, Y.S., Feng, G., Ren, J.S.: A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Trans. Syst., Man, Cybern. B: Syst. Humans 34(3), 406–420 (2004)

    Article  Google Scholar 

  23. Yang, Y.S., Zhou, C.J.: Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach. Inform. Sci. 170, 211–234 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yang, Y.S., Li, T.S., Wang, X.F.: Robust adaptive neural network control for strict-feedback nonlinear systems via small-gain approaches. In Lecture Notes in Computer Science, vol. 3972, pp. 888–897. Springer, Berlin (2006)

    Google Scholar 

  25. Yang, Z.J., Nagai, T., Kanae, S., Wada, K.: Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form. Int. J. Syst. Sci. 38(9), 709–724 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  26. Yao, B., Tomizuka, M.: Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. Automatica 37(9), 1305–1321 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  27. Yip, P.P., Hedrick, J.K.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71(5), 959–979 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7), 1895–1903 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Navigation College, Dalian Maritime University, Dalian, 116026, China

    Tieshan Li

  2. Shanghai Jiao Tong University, Shanghai, China

    Tieshan Li

  3. Marine Engineering College, Dalian Maritime University, Dalian, China

    Dan Wang

  4. Department of Mathematics, Dalian Maritime University, Dalian, 116026, China

    Naxin Chen

Authors
  1. Tieshan Li
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  2. Dan Wang
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  3. Naxin Chen
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Correspondence to Tieshan Li.

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Li, T., Wang, D. & Chen, N. Adaptive fuzzy control of uncertain MIMO non-linear systems in block-triangular forms. Nonlinear Dyn 63, 105–123 (2011). https://doi.org/10.1007/s11071-010-9789-0

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  • DOI: https://doi.org/10.1007/s11071-010-9789-0

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