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Nonlinear Dynamics

, Volume 95, Issue 2, pp 1565–1583 | Cite as

Adaptive fuzzy control of MIMO nonstrict-feedback nonlinear systems with fuzzy dead zones and time delays

  • Hang Su
  • Weihai ZhangEmail author
Original Paper
  • 107 Downloads

Abstract

This paper addresses an adaptive fuzzy control for a class of multi-input and multi-output nonlinear nonstrict-feedback systems with fuzzy dead zones, time delays and immeasurable states. Combining backstepping technique with dynamic surface control, only one adaptive law is required for each subsystem, and the whole design procedure is simplified. Compared with the existing researches on multi-input and multi-output nonlinear systems, the main contributions of this paper lie in that the dead zone models of the developed nonlinear system are fuzzy and uncertain, and the systems under consideration are more general. The designed controller not only guarantees that the given target signals can be tracked within small errors, but also guarantees the boundedness of all the signals in the closed-loop system. Finally, simulation results are depicted to demonstrate the effectiveness of our proposed control algorithm.

Keywords

Adaptive fuzzy control Nonstrict-feedback systems Backstepping Dynamic surface control 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61573227, 61633014, 61703248), the Research Fund for the Taishan Scholar Project of Shandong Province of China, and SDUST Research Fund (No. 2015TDJH105).

References

  1. 1.
    Li, Y.M., Tong, S.C.: Command-filtered-based fuzzy adaptive control design for MIMO-switched nonstrict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 25(3), 668–681 (2017)CrossRefGoogle Scholar
  2. 2.
    Ge, S.S., Li, Z.J.: Robust adaptive control for a class of MIMO nonlinear systems by state and output feedback. IEEE Trans. Autom. Control 59(6), 1624–1629 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chen, B., Lin, C., Liu, X.P., Liu, K.F.: Adaptive fuzzy tracking control for a class of MIMO nonlinear systems in nonstrict-feedback form. IEEE Trans. Cybern. 45(12), 2744–2755 (2015)CrossRefGoogle Scholar
  4. 4.
    Kostarigka, A.K., Rovithakis, G.A.: Adaptive dynamic output feedback neural network control of uncertain MIMO nonlinear systems with prescribed performance. IEEE Trans. Neural Netw. Learn. Syst. 23(1), 138–149 (2012)CrossRefGoogle Scholar
  5. 5.
    Yao, X.M., Park, J.H., Dong, H.R., Guo, L., Lin, X.: Robust adaptive nonsingular terminal sliding mode control for automatic train operation. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2018.2817616 Google Scholar
  6. 6.
    Chen, X.Y., Park, J.H., Cao, J.D., Qiu, J.L.: Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control. Neurocomputing 273(17), 9–21 (2018)CrossRefGoogle Scholar
  7. 7.
    Liu, Y.J., Gao, Y., Tong, S.C., Li, Y.M.: Fuzzy approximation-based adaptive backstepping optimal control for a class of nonlinear discrete-time systems with dead-zone. IEEE Trans. Fuzzy Syst. 24(1), 16–28 (2016)CrossRefGoogle Scholar
  8. 8.
    Wang, T., Zhang, Y.F., Qiu, J.B., Gao, H.J.: Adaptive fuzzy backstepping control for a class of nonlinear systems with smapled and delayed measurements. IEEE Trans. Fuzzy Syst. 23(2), 302–312 (2015)CrossRefGoogle Scholar
  9. 9.
    Li, Y.M., Tong, S.C., Li, T.S.: Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones. IEEE Trans. Fuzzy Syst. 23(4), 1228–1241 (2015)CrossRefGoogle Scholar
  10. 10.
    Zhou, Q., Li, H.Y., Wu, C.W., Wang, L.J., Ahn, C.K.: Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans. Syst., Man Cybern. Syst. 47(8), 1979–1989 (2017)CrossRefGoogle Scholar
  11. 11.
    Li, H.Y., Bai, L., Wang, L.J., Zhou, Q., Wang, H.Q.: Adaptive neural control of uncertain nonstrict-feedback stochastic nonlinear systems with output constraint and unknown dead zone. IEEE Trans. Syst., Man Cybern. Syst. 47(8), 2048–2059 (2017)CrossRefGoogle Scholar
  12. 12.
    Meng, W.C., Yang, Q.M., Sun, Y.X.: Adaptive neural control of nonlinear MIMO systems with time-varying output constraints. IEEE Trans. Neural Netw. Learn. Syst. 26(5), 1074–1085 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Zhou, Q., Wu, C.W., Shi, P.: Observer-based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation. Fuzzy Sets Syst. 316(1), 49–68 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Tong, S.C., Li, Y.M., Feng, G., Li, T.S.: Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems. IEEE Trans. Syst. Man Cybern. B Cybern. 41(4), 1124–1135 (2011)CrossRefGoogle Scholar
  17. 17.
    Shieh, H.J., Hua, C.H.: An intergrator-backstepping-based dynamic surface control method for a two-axis piezoelectric micropositioning stage. IEEE Trans. Control Syst. Technol. 15(5), 916–926 (2007)CrossRefGoogle Scholar
  18. 18.
    Tong, S.C., Sui, S., Li, Y.M.: Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. 23(4), 729–742 (2015)CrossRefGoogle Scholar
  19. 19.
    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(1), 168–180 (2012)CrossRefGoogle Scholar
  20. 20.
    Liu, Y.J., Tong, S.C.: Adaptive fuzzy identification and control for a class of nonlinear pure-feedback MIMO systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 23(5), 1387–1398 (2015)CrossRefGoogle Scholar
  21. 21.
    Hua, C.C., Ding, S.X.: Model following controller design for large-scale systems with time-delay interconnections and multiple dead-zone inputs. IEEE Trans. Autom. Control 56(4), 962–968 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Zhou, N., Liu, Y.J., Tong, S.C.: Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input. Nonlinear Dyn. 63(4), 771–778 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wang, F., Liu, Z., Zhang, Y., Chen, C.L.P.: Adaptive quantized fuzzy control of stochastic nonlinear systems with actuator dead-zone. Inf. Sci. 370–371(20), 385–401 (2016)CrossRefGoogle Scholar
  24. 24.
    Wang, F., Liu, Z., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive fuzzy dynamic surface cotrol for a class of nonlinear systems with fuzzy dead zone and dynamic uncertainties. Nonlinear Dyn. 79(3), 1693–1709 (2015)CrossRefzbMATHGoogle Scholar
  25. 25.
    Na, J., Ren, X.M., Herrmann, G., Qiao, Z.: Adaptive neural dynamic surface control for servo systems with unknwon dead-zone. Control Eng. Pract. 19(11), 1328–1343 (2011)CrossRefGoogle Scholar
  26. 26.
    Peng, J., Dubay, R.: Identification and adaptive neural network control of a DC motor system with dead-zone characteristics. ISA Trans. 50(4), 588–598 (2011)CrossRefGoogle Scholar
  27. 27.
    Xu, B.: Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity. Nonlinear Dyn. 80(3), 1509–1520 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Adaptive fuzzy tracking control of nonlinear MIMO systems with time-varying delays. Fuzzy Sets Syst. 217(16), 1–21 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans. Fuzzy Syst. 18(5), 883–892 (2010)CrossRefGoogle Scholar
  30. 30.
    Li, Y.M., Tong, S.C., Li, T.S.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2015)CrossRefGoogle Scholar
  31. 31.
    Li, Y.M., Tong, S.C., Liu, Y.J., Li, T.S.: Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on small-gain approach. IEEE Trans. Fuzzy Syst. 22(1), 164–176 (2014)CrossRefGoogle Scholar
  32. 32.
    Li, Z., Chen, J., Zhang, G., Gan, M.: Stabilising tracking of uncertain switched non-linear systems in semi-strict feedback form. IET Control Theory Appl. 6(4), 588–595 (2012)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Wang, H.Q., Liu, X.P., Liu, K.F.: Adaptive fuzzy tracking control for a class of pure-feedback stochastic nonlinear systems with non-lower triangular structure. Fuzzy Sets Syst. 302(1), 101–120 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Wang, H.Q., Liu, X.P., Chen, B., Zhou, Q.: Adaptive fuzzy decentralized control for a class of pure-feedback large-scale nonlinear systems. Nonlinear Dyn. 75(3), 449–460 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)CrossRefGoogle Scholar
  36. 36.
    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(5), 972–982 (2011)Google Scholar
  37. 37.
    Li, T.S., Tong, S.C., Feng, G.: A novel robust adaptive-fuzzy-tracking control for a class of nonlinear multi-input/multi-output systems. IEEE Trans. Fuzzy Syst. 18(1), 150–160 (2010)CrossRefGoogle Scholar
  38. 38.
    Zhao, X.D., Yang, H.J., Karimi, H.R., Zhu, Y.Z.: Adaptive neural control of MIMO nonstrict-feedback nonlinear systems with time delay. IEEE Trans. Cybern. 46(6), 1337–1349 (2016)CrossRefGoogle Scholar
  39. 39.
    Jin, X.Z., Wang, S.F., Qin, J.H., Zheng, W.X., Kang, Y.: Adaptive fault-tolerant consensus for a class of uncertain nonlinear second-order multi-agent systems with circuit implementation. IEEE Trans. Circuits Syst. I Reg. Pap. 65(7), 2243–2255 (2018)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Jin, X.Z., Qin, J.H., Shi, Y., Zheng, W.X.: Auxiliary fault tolerant control with actuator amplitude saturation and limited rate. IEEE Trans. Syst. Man Cybern. Syst. (2017).  https://doi.org/10.1109/TSMC.2017.2752961 Google Scholar
  41. 41.
    Shen, H., Li, F., Wu, Z.G., Park, J.H., Sreeram, V.: Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters. IEEE Trans. Fuzzy Syst. (2018).  https://doi.org/10.1109/TFUZZ.2018.2832614 Google Scholar
  42. 42.
    Shen, H., Li, F., Yan, H.C., Karimi, H.R., Lam, H.K.: Finite-time event-triggered \(H_{\infty }\) control for T–S fuzzy Markov jump systems. IEEE Trans. Fuzzy Syst. (2018).  https://doi.org/10.1109/TFUZZ.2017.2788891
  43. 43.
    Su, H., Zhang, W.H.: Adaptive fuzzy FTC design of nonlinear stochastic systems with actuator faults and unmodeled dynamics. Int. J. Adapt. Control Signal Process. 32(7), 1081–1101 (2018)CrossRefzbMATHGoogle Scholar
  44. 44.
    Wang, J., Liang, K., Huang, X., Wang, Z., Shen, H.: Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback. Appl. Math. Comput. 328(1), 247–262 (2018)MathSciNetGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Electrical Engineering and AutomationShandong University of Science and TechnologyQingdaoChina

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