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Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input

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Abstract

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of SISO nonaffine nonlinear systems with unknown dead-zone input and immeasurable states. Within this scheme, the original nonaffine system is firstly transformed into an affine-like form by using Taylor series expansion, the unknown dead-zone input is treated as a combination of a linear and a bounded disturbance-like term, and a state observer is introduced to estimate the system states. The fuzzy logic systems are utilized to directly approximate the desire virtual control law, and a novel adaptive fuzzy output feedback controller is designed via backstepping. A main advantage of the proposed controller is that only one adaptive parameter needs to be updated online in backstepping design process. Theoretically, it is proved that the presented adaptive fuzzy controller can guarantee that the tracking error converges to a small neighborhood of the origin and all signals in closed-loop are bounded. Finally, the simulation results validate the effectiveness of the proposed scheme.

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References

  1. Wang, X.S., Su, C.Y., Hong, H.: Robust adaptive control of a class of linear systems with unknown dead-zone. Automatica 40, 407–413 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ibrir, S., Xie, W.F., Su, C.Y.: Adaptive tracking of nonlinear systems with non-symmetric dead-zone input. Automatica 43, 522–530 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hua, C.C., Wang, Q.G., Guan, X.P.: Adaptive tracking controller design of nonlinear systems with time delays and unknown dead-zone input. IEEE Trans. Autom. Control 53, 1753–1759 (2008)

    Article  MathSciNet  Google Scholar 

  4. Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21, 134–146 (2013)

    Article  Google Scholar 

  5. Adloo, H., Noroozi, N., Karimaghaee, P.: Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity. Nonlinear Dyn. 67, 1337–1356 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kim, J.H., Park, J.H., Lee, S.W., Cheng, E.K.P.: A two layered fuzzy logic controller for systems with dead-zones. IEEE Trans. Ind. Electron. 41, 155–162 (1994)

    Google Scholar 

  7. Lewis, F.L., Tim, W.K., Wang, L.Z., Li, Z.X.: Dead-zone compensation in motion control systems using adaptive fuzzy logic control. IEEE Trans. Control Syst. Technol. 7, 731–742 (1999)

    Article  Google Scholar 

  8. Jang, J.O.: A dead-zone compensator of a DC motor system using fuzzy logic control. IEEE Trans. Man Syst. Cybern. Part C: Appl. Rev. 31, 42–48 (2001)

    Article  Google Scholar 

  9. Cho, H., Bai, E.: Convergence results for an adaptive dead zone inverse. Int. J. Adapt. Control Signal Process. 12, 451–466 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Taware, A., Tao, G., Teolis, C.: Design and analysis of a hybrid control scheme for sandwich nonsmooth nonlinear systems. IEEE Trans. Autom. Control 47, 145–150 (2002)

    Article  MathSciNet  Google Scholar 

  11. Zhou, J., Wen, C.Y., Zhang, Y.: Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Trans. Autom. Control 51, 504–511 (2006)

    Article  MathSciNet  Google Scholar 

  12. Zhou, J., Shen, X.Z.: Robust adaptive control of nonlinear uncertain plants with unknown dead-zone. IET Control Theory Appl. 1, 25–32 (2007)

    Article  MathSciNet  Google Scholar 

  13. Tong, S.C., Li, Y.M.: Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 20, 168–180 (2012)

    Article  Google Scholar 

  14. Tseng, C.S., Chen, B.S., Uang, H.J.: Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model. IEEE Trans. Fuzzy Syst. 9, 381–392 (2001)

    Article  Google Scholar 

  15. Chang, W.J., Sun, C.C.: Constrained fuzzy controller design of discrete Takagi–Sugeno fuzzy models. Fuzzy Sets Syst. 133, 37–55 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 815–821 (2006)

    Google Scholar 

  17. Wu, D.R.: On the fundamental differences between internal type-2 and type-1 fuzzy logic controller. IEEE Trans. Fuzzy Syst. 20, 832–848 (2012)

    Article  Google Scholar 

  18. Abdelnour, G.M.: Design of a fuzzy controller using input and output mapping factors. IEEE Trans. Syst. Man Cybern. 21, 952–960 (1991)

    Article  Google Scholar 

  19. Malki, H.A., Misir, D., Feigenspan, D.: Fuzzy PID Control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans. Control Syst. Technol. 5, 371–378 (1997)

    Article  Google Scholar 

  20. Meza, J., Santibanez, V., Soto, R., Llama, M.: Fuzzy self-tuning pid semiglobal regulator for robot manipulators. IEEE Trans. Ind. Electron. 59, 2709–2717 (2012)

    Article  Google Scholar 

  21. Chen, W.S., Jiao, L.C., Li, R.H., Li, J.: Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Trans. Fuzzy Syst. 18, 674–685 (2010)

    Article  Google Scholar 

  22. Lee, H.: Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 19, 265–275 (2011)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  26. Li, Y.M., Tong, S.C., Li, T.S.: Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash-like hysteresis. Inf. Sci. 198, 130–146 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. Li, Y.M., Ren, C.E., Tong, S.C.: Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer. Nonlinear Dyn. 67, 1175–1191 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. Tong, S.C., Liu, C.L., Li, Y.M.: Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain. Neurocomputing 77, 58–70 (2012)

    Article  Google Scholar 

  29. Jiang, Z., Mareels, I., Hill, D., Huang, J.: A unifying framework for global regulation via nonlinear output feedback: from ISS to IISS. IEEE Trans. Fuzzy Syst. 18, 2360–2365 (2007)

    Google Scholar 

  30. Zhou, Q., Shi, P., Lu, J.J., Xu, S.Y.: Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Trans. Fuzzy Syst. 19, 972–981 (2011)

    Article  Google Scholar 

  31. Zhou, Q., Shi, P., Xu, S.Y., Li, H.Y.: Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 21, 301–312 (2013)

    Article  Google Scholar 

  32. 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.-Part A: Syst. Hum. 34, 406–420 (2004)

    Article  Google Scholar 

  33. Yang, Y.S., Zhou, C.J.: Adaptive fuzzy H\(\infty \) stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach. IEEE Trans. Fuzzy Syst. 13, 104–114 (2005)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  35. Labiod, S., Guerra, T.M.: Indirect adaptive fuzzy control for a class of nonaffine nonlinear systems with unknown control directions. Int. J. Control Autom. Syst. 8, 903–907 (2010)

  36. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  37. Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice Hall, Englewood Cliffs (1997)

    MATH  Google Scholar 

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Authors and Affiliations

  1. College of Automatic, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Wei-Dong Zhou, Cheng-Yi Liao, Lan Zheng & Meng-Meng Liu

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  1. Wei-Dong Zhou
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  2. Cheng-Yi Liao
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  3. Lan Zheng
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  4. Meng-Meng Liu
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Correspondence to Cheng-Yi Liao.

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Zhou, WD., Liao, CY., Zheng, L. et al. Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input. Nonlinear Dyn 79, 2609–2621 (2015). https://doi.org/10.1007/s11071-014-1835-x

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