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Stability Analysis and Dynamic Output Feedback Control for Nonlinear T-S Fuzzy System with Multiple Subsystems and Normalized Membership Functions

  • Wei Zheng
  • Zhi-Ming Zhang
  • Hong-Bin Wang
  • Hong-Rui Wang
  • Peng-Heng Yin
Regular Papers Control Theory and Applications

Abstract

This paper addresses the stability analysis and dynamic output-feedback control problems for a class of nonlinear Takagi-Sugeno (T-S) fuzzy systems with multiple subsystems and normalized membership functions. First, the switching control law of the membership function is proposed based on the membership function for the nonlinear T-S fuzzy subsystems. Secondly, the relaxation parameter is introduced into this switching control law to guarantee a minimal dwell time between two consecutive switching. Then, based on the proposed switching control law of the membership function and relaxation parameter, the dynamic output feedback controller with the estimate algorithm is designed to estimate the attraction domain. By introducing the new switched Lyapunov-Krasovskii functional, it can be seen that the solutions of the resultant closed-loop system converge to an adjustable bounded region. Compared with the previous works, the developed controller in this paper is flexible and smooth, which only uses the system output. And the results are further extended to the mobile robot case and the chemical process case. Finally, two simulation examples are performed to show the effectiveness of the theoretical results.

Keywords

Dynamic output-feedback Lyapunov-Krasovskii functional multiple subsystems relaxation parameter switching control law T-S fuzzy system 

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References

  1. [1]
    S. Park, H. Lee, S. Han, and J. Lee, “Adaptive fuzzy supertwisting backstepping control design for MIMO nonlinear strict feedback systems,” International Journal of Control Automation & Systems, vol. 16, no. 3, pp. 1165–1178, April 2018.CrossRefGoogle Scholar
  2. [2]
    J. B. Qiu, S. X. Ding, L. L. Li, and S. N. Yin, “Reliable fuzzy output feedback control of nonlinear parabolic distributed parameter systems with sensor faults1,” Journal of Intelligent & Fuzzy Systems, vol. 29, no. 3, pp. 1197–1208, October 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    C. C. Hua, Q. G. Wang, and X. P. Guan, “Adaptive fuzzy output-feedback controller design for nonlinear time-delay systems with unknown control direction,” IEEE Transactions on Systems Man & Cybernetics Part B, vol. 39, no.2, pp. 363–374, April 2009.Google Scholar
  4. [4]
    C. C. Hua and X. P. Guan, “Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties,” Automatica, vol. 68, pp. 1–8, June 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Y. L. Wei, J. B. Qiu, P. Shi, and M. Chadli, “Fixed-order piecewise-affine output feedback controller for fuzzyaffine-model-based nonlinear systems with time-varying delay,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 64, no.4, pp. 945–958, April 2017.Google Scholar
  6. [6]
    Y. L. Wei, J. B. Qiu, and H. R. Karimi, “Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults,” IEEE Transactions on Circuits & Systems I Regular Papers, vol. 64, no. 1 pp. 170–181, July 2017.Google Scholar
  7. [7]
    Y. L. Wei, J. B. Qiu, P. Shi, and H. K. Lam, “A new design of H-infinity piecewise filtering for discrete-time nonlinear time-varying delay systems via T-S fuzzy affine models,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 47 no. 8, pp. 2034–2047, August 2017.Google Scholar
  8. [8]
    C. Z. Zhang, J. F. Hu, J. B. Qiu, and Q. J. Chen, “Eventtriggered nonsynchronized H-filtering for discrete-time TS fuzzy systems based on piecewise Lyapunov functions,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 47, no. 8, pp. 2330–2341, August 2017.CrossRefGoogle Scholar
  9. [9]
    W. Yu, F. O. Rodríguez, and M. Armendariz, “Hierarchical fuzzy CMAC for nonlinear systems modeling,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 5, pp. 1302–1314, June 2008.CrossRefGoogle Scholar
  10. [10]
    J. L. Chang and T. C. Wu, “Disturbance observer based output feedback controller design for systems with mismatched disturbance,” International Journal of Control Automation & Systems, vol. 16, no. 4, pp. 1775–1782, July 2018.MathSciNetCrossRefGoogle Scholar
  11. [11]
    C. Z. Zhang, J. F. Hu, J. B. Qiu, and Q. J. Chen, “Reliable output feedback control for T-S fuzzy systems with decentralized event triggering communication and actuator failures,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2592–2602, February 2017.CrossRefGoogle Scholar
  12. [12]
    G. B. Koo, B. P. Jin, and Y. H. Joo, “Intelligent digital redesign for sampled-data fuzzy control systems based on state-matching error cost function approach,” International Journal of Control Automation & Systems, vol. 16, no. 1, pp. 350–359, March 2018.CrossRefGoogle Scholar
  13. [13]
    C. J. Lee and M. T. Lim, “Fuzzy FIR filtering for TS fuzzy systems with quantization and packet dropout,” International Journal of Control Automation & Systems, vol. 13, no. 3, pp. 961–971, May 2018.CrossRefGoogle Scholar
  14. [14]
    S. C. Tong, Y. M. Li, G. Feng, and T. S. Li, “Observerbased adaptive fuzzy back-stepping dynamic surface control for a class of MIMO nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 41, no. 4, pp. 1124–1135, August 2011.CrossRefGoogle Scholar
  15. [15]
    Y. Li, Y. M. Li, and S. C. Tong, “Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large-scale systems,” Neurocomputing, vol. 23, no. 4, pp. 381–399, April 2013.zbMATHGoogle Scholar
  16. [16]
    Y. L. Wei, J. B. Qiu, H. K. Lam, and L. G. Wu, “Approaches to T-S fuzzy-affine-model-based reliable output feedback control for nonlinear Ito stochastic systems,” IEEE Transactions on fuzzy systems, vol. 25, no. 3, pp. 569–583, May 2017.CrossRefGoogle Scholar
  17. [17]
    T. C. Wang and S. C. Tong, “Observer-based outputfeedback asynchronous control for switched fuzzy systems,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2579–2591, May 2017.CrossRefGoogle Scholar
  18. [18]
    C. J. Lee and M. T. Lim, “Synergetic adaptive fuzzy control for a class of nonlinear discrete-time systems,” International Journal of Control Automation & Systems, vol. 16, no. 4, pp. 1981–1988, July 2018.CrossRefGoogle Scholar
  19. [19]
    Y. M. Li, S. C. Tong, L. Liu, and G. Feng, “Adaptive output-feedback control design with prescribed performance for switched nonlinear systems,” Automatica, vol. 80, pp. 225–231, June 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    D. Zhai, A. Y. Lu, J. H. Li, and Q. L. Zhang, “Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time,” Applied Mathematics & Computation, vol. 273, pp. 767–792, January 2016.MathSciNetCrossRefGoogle Scholar
  21. [21]
    S. C. Tong, L. L. Zhang, and Y. M. Li, “Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 46, no. 1, pp. 37–47, January 2016.CrossRefGoogle Scholar
  22. [22]
    T. Wang, Y. F. Zhang, J. B. Qiu, and H. J. Gao, “Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 2, pp. 302–312, April 2015.CrossRefGoogle Scholar
  23. [23]
    Y. N. Sun, G. B. Koo, B. P. Jin, and Y. H. Joo, “I-¥ adaptive fuzzy filter design for nonlinear systems with missing measurements: fuzzy basis-dependent Lyapunov function approach,” International Journal of Control Automation & Systems, vol. 14, no. 2, pp. 425–434, Febrary 2017.Google Scholar
  24. [24]
    C.W. Wu, J. X. Liu, Y. Y. Xiong, and L. G. Wu, “Observerbased adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems,” IEEE Transactions on Neural Networks & Learning Systems, vol. 29, no. 7, pp. 3022–3033, July 2018.MathSciNetGoogle Scholar
  25. [25]
    C. W. Wu, J. X. Liu, X. J. Jing, H. Y. Li, and L. G. Wu, “Adaptive fuzzy control for nonlinear networked control systems,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 47, no. 8, pp. 2420–2430, August 2017.CrossRefGoogle Scholar
  26. [26]
    Q. Zhou, H. Y. Li, L. J. Wang, and R. Q. Lu, “Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 48, no. 10, pp. 1747–1758, October 2018.CrossRefGoogle Scholar
  27. [27]
    J. B. Qiu, S. X. Ding, H. J. Gao, and S. Yin, “Fuzzy-modelbased reliable static output feedback H-¥ control of nonlinear hyperbolic PDE systems,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 2, pp. 388–400, April 2016.CrossRefGoogle Scholar
  28. [28]
    Y. M. Li, S. C. Tong, Y. J. Liu, and T. Li, “Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small-gain approach,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 164–176, February 2014.CrossRefGoogle Scholar
  29. [29]
    S. C. Tong, S. Sui, and Y. Li, “Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 729–742, August 2015.CrossRefGoogle Scholar
  30. [30]
    Y. M. Li and S. C. Tong, “Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrictfeedback nonlinear systems,” IEEE Transactions on Cybernetics, vol. 47, no. 4, pp. 1007–1016, April 2017.CrossRefGoogle Scholar
  31. [31]
    T. Wang, J. B. Qiu, H. J. Gao, and C. H. Wang, “Networkbased fuzzy control for nonlinear industrial processes with predictive compensation strategy,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 47, no. 8, pp. 2137–2147, August 2017.CrossRefGoogle Scholar
  32. [32]
    J. B. Qiu, G. Feng, and H. Gao, “Static-output-feedback control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 2, pp. 245–261, April 2013.CrossRefGoogle Scholar
  33. [33]
    T. Wang, J. B. Qiu, S. S. Fu, and W. Q. Ji, “Distributed fuzzy H-¥ filtering for nonlinear multirate networked double-layer industrial processes,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 5203–5211, June 2017.CrossRefGoogle Scholar
  34. [34]
    T. Wang, H. J. Gao, and J. B. Qiu, “A combined faulttolerant and predictive control for network-based industrial processes,” IEEE Transactions on Industrial Electronics, vol. 63, no. 4, pp. 2529–2536, April 2016.Google Scholar
  35. [35]
    H. Y. Li, C. Wu, and Z. Feng, “Fuzzy dynamic outputfeedback control of non-linear networked discrete-time system with missing measurements,” IET Control Theory & Applications, vol. 9, no. 3, pp. 327–335, February 2015.MathSciNetCrossRefGoogle Scholar
  36. [36]
    Y. L. Wei, J. B. Qiu, H. R. Karimi, and M. Wang, “New results on H-¥ dynamic output feedback control for Markovian jump systems with time-varying delay and defective mode information,” Optimal Control Applications & Methods, vol. 35, no. 6, pp. 656–675, November 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    X. H. Chang, J. Xiong, and J. H. Park, “Fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties,” Applied Mathematics & Computation, vol. 291, pp. 213–225, December 2016.MathSciNetCrossRefGoogle Scholar
  38. [38]
    D. H. Lee, J. B. Park, and Y. H. Joo, “A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems,” Information Sciences, vol. 185, no. 1, pp. 230–248, February 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    A. Zemouche and M. Boutayeb, “On LMI conditions to design observers for Lipschitz nonlinear systems,” Automatica, vol. 49, no. 2, pp. 585–591, February 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    D. Zhai, A. Y. Lu, J. Dong, and Q. L. Zhang, “Stability analysis and state feedback control of continuous-time T-S fuzzy systems via anew switched fuzzy Lyapunov function approach,” Applied Mathematics & Computation, vol. 293, no. C, pp. 586–599, January 2017.Google Scholar
  41. [41]
    M. B. Yazdi and M. R. Jahed-Motlagh, “Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization,” Chemical Engineering Journal, vol. 155, no. 3, pp. 838–843, December 2016.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Wei Zheng
    • 1
  • Zhi-Ming Zhang
    • 1
  • Hong-Bin Wang
    • 1
  • Hong-Rui Wang
    • 2
  • Peng-Heng Yin
    • 1
  1. 1.School of Electric EngineeringYanshan UniversityQinhuangdaoP. R. China
  2. 2.School of Electronic and Information EngineeringHebei UniversityBaodingP. R. China

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