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Observer-Based Adaptive Fuzzy Tracking Control for a Class of Strict-Feedback Systems with Event-Triggered Strategy and Tan-type Barrier Lyapunov Function

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Abstract

In this paper, an observer-based adaptive fuzzy tracking control is considered for a class of strict-feedback nonlinear systems. The nonlinear functions and unmeasured states in the system are estimated by means of fuzzy logic systems and fuzzy state observers, respectively. In addition, the tan-type barrier Lyapunov specifies that the tracking error is limited to a given area. An improved event-triggered technique is introduced in the controller design to save the network resources and avoid the Zeno-behavior. It is proven that the proposed controller can ensure that all the signals of the closed-loop system are uniformly and ultimately bounded. Finally, the simulation results verify the feasibility of the design scheme.

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References

  1. Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control. 52(9), 1680–1685 (2007)

    Article  MathSciNet  Google Scholar 

  2. Postoyan, R., Tabuada, P., Nesic, D., Anta, A.: A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Autom. Control. 60(4), 982–996 (2015)

    Article  MathSciNet  Google Scholar 

  3. Heemels, W. P. M. H., Johansson, K. H., Tabuada, P.: An introduction to event-triggered and self-triggered control. In: Proceedings of the 51st IEEE Conference on Decision and Control. p. 3270–3285 (2012)

  4. Wang, X., Lemmon, M.D.: Event-triggering in distributed networked control systems. IEEE Trans. Autom. Control. 56(3), 586–601 (2011)

    Article  MathSciNet  Google Scholar 

  5. Adaldo, A., Alderisio, F., Liuzza, D., Shi, G., Johansson, K. H.: Event-triggered pinning control of complex networks with switching topologies. In: Proceedings of the 53rd IEEE Conference on Decision and Control. (2014)

  6. Adaldo, A., Alderisio, F., Liuzza, D., Shi, G., Johansson, K.H.: Event-triggered pinning control of switching networks. IEEE Trans. Control Netw. Syst. 2(2), 1–1 (2015)

    Article  MathSciNet  Google Scholar 

  7. Yook, J.K., Tilbury, D.M., Soparkar, N.R.: Trading computation for bandwidth: reducing communication in distributed control systems using state estimators. IEEE Trans. Control Syst. Technol. 10(4), 503–518 (2002)

    Article  Google Scholar 

  8. Liu, C., Wang, H., Liu, X., Zhou, Y., Lu, S.: Event-triggered adaptive tracking control for uncertain nonlinear systems based on a new funnel function. ISA Trans. 99, 130–138 (2020)

    Article  Google Scholar 

  9. Li, Y., Tong, S., Li, T.: Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems. Nonlinear Anal. Hybrid Syst. 16, 72–80 (2015)

    Article  MathSciNet  Google Scholar 

  10. Xing, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control. 62(4), 2071–2076 (2017)

    Article  MathSciNet  Google Scholar 

  11. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and adaptive control design. Wiley, New York (1995)

    MATH  Google Scholar 

  12. Tong, S., Li, Y.: Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci. China Inform. Sci. 53(2), 307–324 (2010)

    Article  MathSciNet  Google Scholar 

  13. Wang, F., Zhang, X.: Adaptive finite time control of nonlinear systems under time-varying actuator failures. IEEE Trans. Syst. Man Cybern. Syst. 49(9), 1845–1852 (2019)

    Article  Google Scholar 

  14. Tong, S., Li, Y., Xu, Y.: Prescribed performance fuzzy adaptive fault-tolerant control of non-linear systems with actuator faults. IET Control Theory Appl. 8(6), 420–431 (2014)

    Article  MathSciNet  Google Scholar 

  15. Liu, C., Wang, H., Liu, X., Zhou, Y., Lu, S.: Adaptive prescribed performance tracking control for strict-feedback nonlinear systems with zero dynamics. Int. J. Robust Nonlinear (2019). https://doi.org/10.1002/rnc.4739

    Article  MATH  Google Scholar 

  16. 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)

    MathSciNet  Google Scholar 

  17. Hsiao, M.Y., Chen, C.Y., Li, T.H.S.: Interval type-2 adaptive fuzzy sliding-mode dynamic control design for wheeled mobile robots. Int. J. Fuzzy Syst. 10(4), 268–275 (2008)

    MathSciNet  Google Scholar 

  18. Wang, F., Chen, B., Sun, Y., Gao, Y., Lin, C.: Finite-time fuzzy control of stochastic nonlinear systems. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2925573

    Article  Google Scholar 

  19. Leu, Y.G., Lee, T.T., Wang, W.Y.: Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems. IEEE Trans. Cybern. 29(5), 583–591 (1999)

    Article  Google Scholar 

  20. Liu, C., Wang, H., Liu, X., Zhou, Y.: Adaptive finite-time fuzzy funnel control for nonaffine nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2917547

    Article  Google Scholar 

  21. Wang, H., Liu, X., Zhao, X.: Adaptive fuzzy finite-time control of nonlinear systems with actuator faults. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TCYB.2019.2902868

    Article  Google Scholar 

  22. Wang, H., Chen, B., Lin, C.: Direct adaptive neural tracking control for a class of stochastic pure-feedback nonlinear systems with unknown dead-zone. Int. J. Adapt Control. 27(4), 302–322 (2013)

    Article  MathSciNet  Google Scholar 

  23. Wang, H., Liu, P.X., Xie, X., Hayat, T., Alsaadi, F.: Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator. Inf. Sci. (2018). https://doi.org/10.1016/j.ins.2018.04.011

    Article  Google Scholar 

  24. Xie, X., Dong, Y., Chen, P.: Relaxed real-time scheduling stabilization of discrete-time takagi-sugeno fuzzy systems via an alterable-weights-based ranking switching mechanism. IEEE Trans. Fuzzy Syst. 26(6), 3808–3819 (2018)

    Article  Google Scholar 

  25. Xie, X., Dong, Y., Chen, P.: Observer design of discrete-time fuzzy systems based on an alterable weights method. IEEE Trans. Cybern. 47(9), 2425–2436 (2018)

    Google Scholar 

  26. Li, Y., Qu, F., Tong, S.: Observer-based fuzzy adaptive finite time containment control of nonlinear multi-agent systems with input-delay. IEEE Trans. Cybern. 1–12, 99 (2020)

    Google Scholar 

  27. Tong, S., Li, Y.: Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems. Sci. China Inform. Sci. 57(1), 1–14 (2014)

    Article  MathSciNet  Google Scholar 

  28. Liu, Y., Tong, S.: Barrier lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica. 64(3), 70–75 (2016)

    Article  MathSciNet  Google Scholar 

  29. Wang, C., Wu, Y., Yu, J.: Barrier lyapunov functions-based dynamic surface control for pure-feedback systems with full state constraints. IET Control Theory Appl. 11(4), 524–530 (2017)

    Article  MathSciNet  Google Scholar 

  30. 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)

    Article  MathSciNet  Google Scholar 

  31. Zhang, J., Yang, G.: Prescribed performance fault-tolerant control of uncertain nonlinear systems with unknown control directions. IEEE Trans. Autom. Control. 62(12), 6529–6535 (2017)

    Article  MathSciNet  Google Scholar 

  32. Cao, J., Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. 52(2), 417–426 (2005)

    Article  MathSciNet  Google Scholar 

  33. Hua, C.C., Wang, Q.G., Guan, X.P.: Adaptive fuzzy output-feedback controller design for nonlinear time-delay systems with unknown control direction. IEEE Trans. Cybern. 39(2), 363–374 (2009)

    Article  Google Scholar 

  34. Wang, L.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)

    Article  Google Scholar 

  35. Polycarpou, M.M., Ioannou, P.A.: A robust adaptive nonlinear control design. Automatica. 32(3), 423–427 (1996)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported in part by Excellent Talents Training Program of University of Science and Technology Liaoning (Grant No. 2019RC09) and the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, 114051, Liaoning, China

    Chuang Gao, Xin Zhou, Yonghui Yang & Zhigang Li

  2. Faculty of Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada

    Xiaoping Liu

Authors
  1. Chuang Gao
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  2. Xin Zhou
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  3. Xiaoping Liu
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  4. Yonghui Yang
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  5. Zhigang Li
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Correspondence to Zhigang Li.

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Gao, C., Zhou, X., Liu, X. et al. Observer-Based Adaptive Fuzzy Tracking Control for a Class of Strict-Feedback Systems with Event-Triggered Strategy and Tan-type Barrier Lyapunov Function. Int. J. Fuzzy Syst. 22, 2534–2545 (2020). https://doi.org/10.1007/s40815-020-00948-0

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  • DOI: https://doi.org/10.1007/s40815-020-00948-0

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