Advertisement

International Journal of Fuzzy Systems

, Volume 21, Issue 3, pp 733–744 | Cite as

Observer-Based Adaptive Fuzzy Control for Time-Varying State Constrained Strict-Feedback Nonlinear Systems with Dead-Zone

  • Peihao Du
  • Kai Sun
  • Shiyi Zhao
  • Hongjing LiangEmail author
Article
  • 106 Downloads

Abstract

This paper focuses on the problem of adaptive fuzzy control for a class of time-varying state constrained strict-feedback nonlinear systems with dead-zone. Based on the arbitrary approximation of fuzzy logic systems (FLSs), the unknown nonlinear functions in the system are approximated by FLSs. Time-varying barrier Lyapunov functions and a fuzzy observer are designed to dispose the unmeasured time-varying constrained states in the system. Furthermore, combining with the adaptive backstepping method and Lyapunov stability theory, it is testified that the proposed control strategy can ensure system stability and all the signals in the closed-loop system are semi-global uniformly ultimately bounded. Finally, the simulation results are given to demonstrate the effectiveness of the proposed method.

Keywords

Nonlinear systems Adaptive fuzzy control Fuzzy state observer Time-varying state constraints Dead-zone 

Notes

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (61703051), the Department of Education of Liaoning Province (LZ2017001), and the PhD Start-up Fund of Liaoning Province (20170520124).

References

  1. 1.
    Tong, S., Li, Y.: Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749–1764 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Liu, D., Xu, Y., Wei, Q., Liu, X.: Residential energy scheduling for variable weather solar energy based on adaptive dynamic programming. IEEE/CAA J. Autom. Sin. 5(1), 36–46 (2018)CrossRefGoogle Scholar
  3. 3.
    Wang, N., Meng, J.E.: Direct adaptive fuzzy tracking control of marine vehicles with fully unknown parametric dynamics and uncertainties. IEEE Trans. Control Syst. Technol. 24(5), 1845–1852 (2016)CrossRefGoogle Scholar
  4. 4.
    Zhang, Y., Liang, H., Ma, H., Zhou, Q., Yu, Z.: Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints. Appl. Math. Comput. 326, 16–32 (2018)MathSciNetGoogle Scholar
  5. 5.
    Zhang, Y., Sun, J., Liang, H., Li, H.: Event-triggered adaptive tracking control for multi-agent systems with unknown disturbances. IEEE Trans. Cybern. (2018).  https://doi.org/10.1109/TCYB.2018.2869084 Google Scholar
  6. 6.
    Ma, H., Liang, H., Ma, H., Zhou, Q.: Nussbaum gain adaptive backstepping control of nonlinear strict-feedback systems with unmodeled dynamics and unknown dead-zone. Int. J. Robust Nonlinear Control (2018).  https://doi.org/10.1002/rnc.4315 MathSciNetGoogle Scholar
  7. 7.
    Zhou, Q., Li, H., Wu, C., Wang, L., 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
  8. 8.
    Sakthivel, R., Ahn, C.K., Joby, M.: Fault-tolerant resilient control for fuzzy fractional order systems. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2018.2835442 Google Scholar
  9. 9.
    Tong, S., Sun, K., Sui, S.: Observer-based adaptive fuzzy decentralized optimal control design for strict-feedback nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 26(2), 569–584 (2018)CrossRefGoogle Scholar
  10. 10.
    Ma, H., Liang, H., Zhou, Q., Ahn, C.K.: Adaptive dynamic surface control design for uncertain nonlinear strict-feedback systems with unknown control direction and disturbances. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2018.2855170 Google Scholar
  11. 11.
    Wei, J., Zhang, Y., Bao, H.: An exploration on adaptive iterative learning control for a class of commensurate high-order uncertain nonlinear fractional order systems. IEEE/CAA J. Autom. Sin. 5(2), 618–627 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lv, W., Wang, F.: Finite-time adaptive fuzzy tracking control for a class of nonlinear systems with unknown hysteresis. Int. J. Fuzzy Syst. 20(3), 782–790 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lin, Z., Liu, X., Li, Y.: Adaptive fuzzy control for nonlinear pure-feedback systems with external disturbance and unknown dead zone output. Int. J. Fuzzy Syst. 19(6), 1940–1949 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Niu, B., Karimi, H.R., Wang, H., Liu, Y.: Adaptive output-feedback controller design for switched nonlinear stochastic systems with a modified average dwell-time method. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1371–1382 (2017)CrossRefGoogle Scholar
  15. 15.
    Chen, B., Liu, X., Lin, C.: Observer and adaptive fuzzy control design for nonlinear strict-feedback systems with unknown virtual control coefficients. IEEE Trans. Fuzzy Syst. 26(3), 1732–1743 (2018)CrossRefGoogle Scholar
  16. 16.
    Yang, C., Ge, S.S., Xiang, C., Chai, T., Lee, T.H.: Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach. IEEE Trans. Neural Netw. 19(11), 1873–1886 (2008)CrossRefGoogle Scholar
  17. 17.
    Vance, J., Jagannathan, S.: Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form. Automatica 44(4), 1020–1027 (2008)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yang, H., Liu, J.: An adaptive RBF neural network control method for a class of nonlinear systems. IEEE/CAA J. Autom. Sin. 5(2), 457–462 (2018)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhao, S., Liang, H., Du, P., Qi, S.: Adaptive NN finite-time tracking control of output constrained nonlinear system with input saturation. Nonlinear Dyn. 92(4), 1845–1856 (2018)CrossRefGoogle Scholar
  20. 20.
    Liu, Y., Gao, Y., Tong, S., Li, Y.: 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
  21. 21.
    Tong, S., Li, Y., Sui, S.: Adaptive fuzzy tracking control design for uncertain non-strict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)CrossRefGoogle Scholar
  22. 22.
    He, W., Huang, B., Dong, Y., Li, z, Su, C.: Adaptive neural network control for a robotic manipulator with unknown dead-zone. IEEE Trans. Cybern. 48(9), 2670–2682 (2018)CrossRefGoogle Scholar
  23. 23.
    Liu, H., Li, S., Li, G., Wang, H.: Adaptive controller design for a class of uncertain fractional-order nonlinear systems: an adaptive fuzzy approach. Int. J. Fuzzy Syst. 20(9), 1–14 (2017)MathSciNetGoogle Scholar
  24. 24.
    Li, Y., Tong, S., Li, T.: Adaptive fuzzy backstepping decentralized control for nonlinear large-scale systems based on DSC technique and high-gain filters. Int. Conf. Fuzzy Theory Appl. (2013).  https://doi.org/10.1109/iFUZZY.2012.6409667 Google Scholar
  25. 25.
    He, W., Chen, Y., Yin, Z.: Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans. Cybern. 46(3), 620–629 (2016)CrossRefGoogle Scholar
  26. 26.
    Yi, J., Li, J., Li, J.: Adaptive fuzzy output feedback control for nonlinear nonstrict-feedback time-delay systems with full state constraints. Int. J. Fuzzy Syst. 20(6), 1730–1744 (2018)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Liu, Y., Tong, S.: Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76, 143–152 (2017)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Tee, K.P., Ren, B., Ge, S.S.: Control of nonlinear systems with time-varying output constraints. Automatica 47(11), 2511–2516 (2011)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Dehaan, D., Guay, M.: Extremum-seeking control of state constrained nonlinear systems. Automatica 41(9), 1567–1574 (2005)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Tee, K.P., Ge, S.S.: Control of nonlinear systems with partial state constraints using a barrier Lyapunov function. Int. J. Control 84(12), 2008–2023 (2011)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Liu, Y., Tong, S.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Lu, S., Li, D., Liu, Y.: Adaptive neural network control for uncertain time-varying state constrained robotics systems. IEEE Trans. Syst. Man Cybern. Syst. (2017).  https://doi.org/10.1109/TSMC.2017.2755377 Google Scholar
  34. 34.
    Li, D., Li, D., Liu, Y., Tong, S., Chen, C.L.P.: Approximation-based adaptive neural tracking control of nonlinear MIMO unknown time-varying delay systems with full state constraints. IEEE Trans. Cybern. 47(10), 3100–3109 (2017)CrossRefGoogle Scholar
  35. 35.
    Wang, L., Lam, H.K.: Local stabilization for continuous-time Takagi–Sugeno fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 26(1), 379–385 (2018)CrossRefGoogle Scholar
  36. 36.
    Xie, X., Yue, D., Zhang, H., Peng, C.: Control synthesis of discrete-time T–S fuzzy systems: reducing the conservatism whilst alleviating the computational burden. IEEE Trans. Cybern. 47(9), 2480–2491 (2017)CrossRefGoogle Scholar
  37. 37.
    Wang, L., Lam, H.K.: A new approach to stability and stabilization analysis for continuous-time Takagi–Sugeno fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 26(4), 2460–2465 (2018)CrossRefGoogle Scholar
  38. 38.
    Xie, X., Yue, D., Peng, C.: Multi-instant observer design of discrete-time fuzzy systems: a ranking-based switching approach. IEEE Trans. Fuzzy Syst. 25(5), 1281–1292 (2017)CrossRefGoogle Scholar
  39. 39.
    Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: Design of a unified adaptive fuzzy observer for uncertain nonlinear systems. Inf. Sci. 265, 139–153 (2014)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Tong, S., Li, Y.: 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
  41. 41.
    Wang, N., Tong, S., Li, Y.: Observer-based adaptive fuzzy control of nonlinear non-strict feedback system with input delay. Int. J. Fuzzy Syst. 20(1), 236–245 (2018)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Wang, N., Gao, Y., Sun, Z., Zheng, Z.: Nussbaum-based adaptive fuzzy tracking control of unmanned surface vehicles with fully unknown dynamics and complex input nonlinearities. Int. J. Fuzzy Syst. 20(1), 259–268 (2018)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Liu, Y., Tong, S., Chen, C.L.P.: Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. 21(2), 275–288 (2013)CrossRefGoogle Scholar
  44. 44.
    Chadli, M., Karimi, H.R.: Robust observer design for unknown inputs Takagi–Sugeno models. IEEE Trans. Fuzzy Syst. 21(1), 158–164 (2013)CrossRefGoogle Scholar
  45. 45.
    Li, Y., Tong, S., Liu, Y., Li, T.: Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small-gain approach. IEEE Trans. Fuzzy Syst. 22(1), 164–176 (2014)CrossRefGoogle Scholar
  46. 46.
    Ma, H., Zhou, Q., Bai, L., Liang, H.: Observer-based adaptive fuzzy fault-tolerant control for stochastic nonstrict-feedback nonlinear systems with input quantization. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2018.2833872 Google Scholar
  47. 47.
    Tong, M., Pan, Y., Li, Z., Lin, W.: Valid data based normalized cross-correlation (VDNCC) for topography identification. Neurocomputing (2018).  https://doi.org/10.1016/j.neucom.2018.04.059 Google Scholar
  48. 48.
    Yang, J., Tong, S.: Observer-based output-feedback control design for a class of nonlinear switched T–S fuzzy systems with actuator saturation and time delay. Int. J. Fuzzy Syst. 19(5), 1333–1343 (2017)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Lu, S., Li, D.: Adaptive neural network control for nonlinear hydraulic servo-system with time-varying state constraints. Complexity (2017).  https://doi.org/10.1155/2017/6893521 MathSciNetGoogle Scholar
  50. 50.
    He, W., Zhang, S., Ge, S.S.: Adaptive control of a flexible crane system with the boundary output constraint. IEEE Ind. Electron. Soc. 61(8), 4126–4133 (2014)CrossRefGoogle Scholar
  51. 51.
    Chen, B., Liu, X., Liu, K., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems. Fuzzy Sets Syst. 159(8), 926–948 (2008)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Zhang, Z., Zhou, Q., Wu, C., Li, H.: Dissipativity-based reliable interval type-2 fuzzy filter design for uncertain nonlinear systems. Int. J. Fuzzy Syst. 20(2), 390–402 (2018)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Yin, S., Wang, G., Karimi, H.R.: Data-driven design of robust fault detection system for wind turbines. Mechatronics 24(4), 298–306 (2014)CrossRefGoogle Scholar
  55. 55.
    Aouaouda, S., Chadli, M., Shi, P., Karimi, H.R.: Discrete-time \(H_{-}/H_{\infty }\) sensor fault detection observer design for nonlinear systems with parameter uncertainty. Int. J. Robust Nonlinear Control 25(3), 339–361 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsBohai UniversityJinzhouChina
  2. 2.College of EngineeringBohai UniversityJinzhouChina

Personalised recommendations