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Adaptive neural-based control for non-strict feedback systems with full-state constraints and unmodeled dynamics

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Abstract

In this paper, an adaptive neural network controller is designed for non-strict feedback systems with full-state constraints. According to practical applications, both input saturation and unmodeled dynamics are also taken into account. By using a logarithm nonlinear mapping, non-strict feedback systems with full-state constraints can be converted to unconstrained ones, which may result in some exponential terms. Here, a new variable separation method is proposed based on Taylor’s formula to cope with the exponential terms and non-strict structure. Then, the relationship between the norm of state vector and error functions is established. A hyperbolic tangent function and a dynamic signal are introduced to deal with input saturation and unmodeled dynamics, respectively. It is proved that all signals of the closed-loop system are uniformly ultimately bounded and the requirement of full-state constraints is satisfied. Two illustrative examples are provided to demonstrate the effectiveness of the presented method.

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References

  1. Zhang, T., Xia, M., Yi, Y.: Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics. Automatica 81, 232–239 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ye, D., Diao, N.N., Zhao, X.G.: Fault-tolerant controller design for general polynomial-fuzzy-model-based systems. IEEE Trans. Fuzzy Syst. 26(2), 1046–1051 (2018)

    Article  Google Scholar 

  3. Kim, M., Grider, K.V.: Terminal guidance for impact attitude angle constrained flight trajectories. IEEE Trans. Aerosp. Electron. Syst. 6, 852–859 (1973)

    Article  Google Scholar 

  4. 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  MATH  Google Scholar 

  5. Yang, H., Ye, D.: Adaptive fixed-time bipartite tracking consensus control for unknown nonlinear multi-agent systems: an information classification mechanism. Inf. Sci. 459, 238–254 (2018)

    Article  MathSciNet  Google Scholar 

  6. Sanner, R.M., Slotine, J.J.: Gaussian networks for direct adaptive control. IEEE Trans. Neural Netw. 3(6), 837–863 (1992)

    Article  Google Scholar 

  7. Ding, S., Wang, J., Zheng, W.X.: Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions. IEEE Trans. Ind. Electron. 62(9), 5899–5909 (2015)

    Article  Google Scholar 

  8. Zhang, T., Ge, S.S., Hang, C.C.: Adaptive neural network control for strict-feedback nonlinear systems using backstepping design. Automatica 36(12), 1835–1846 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Miao, B., Li, T.: A novel neural network-based adaptive control for a class of uncertain nonlinear systems in strict-feedback form. Nonlinear Dyn. 79(2), 1005–1013 (2015)

    Article  MathSciNet  Google Scholar 

  10. Ge, S.S., Wang, C.: Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38(4), 671–682 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhang, T.P., Wen, H., Zhu, Q.: Adaptive fuzzy control of nonlinear systems in pure feedback form based on input-to-state stability. IEEE Trans. Fuzzy Syst. 18(1), 80–93 (2010)

    Article  Google Scholar 

  12. Si, W., Dong, X., Yang, F.: Nussbaum gain adaptive neural control for stochastic pure-feedback nonlinear time-delay systems with full-state constraints. Neurocomputing 292, 130–141 (2018)

    Article  Google Scholar 

  13. Wang, H., Liu, X., Liu, K., Karimi, H.R.: Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. 23(5), 1746–1760 (2015)

    Article  Google Scholar 

  14. Zhou, Q., Wang, L., Wu, C., Li, H., Du, H.: Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint. IEEE Trans. Syst. Man Cybern. Syst. 47(1), 1–12 (2017)

    Article  Google Scholar 

  15. Chen, B., Liu, X.P., Ge, S.S., Lin, C.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. He, W., David, A.O., Yin, Z., Sun, C.: Neural network control of a robotic manipulator with input deadzone and output constraint. IEEE Trans. Syst. Man Cybern. Syst. 46(6), 759–770 (2016)

    Article  Google Scholar 

  18. Ngo, K.B., Mahony, R., Jiang, Z.P.: Integrator backstepping design for motion systems with velocity constraint. In: 5th Asian Control Conference, Melbourne, Victoria (2004)

  19. Ye, D., Zhang, T.Y.: Summation detector for false data injection attack in cyber-physical systems. IEEE Trans. Cybern. 1, 11 (2019). https://doi.org/10.1109/TCYB.2019.2915124

    Article  Google Scholar 

  20. Ye, D., Zhang, T.Y., Guo, G.: Stochastic coding detection scheme in cyber-physical systems against replay attack. Inf. Sci. 481, 432–444 (2019)

    Article  MathSciNet  Google Scholar 

  21. Ni, J., Liu, L., He, W., Liu, C.: Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints. Nonlinear Dyn. 29, 1–20 (2018)

    MATH  Google Scholar 

  22. Li, H., Bai, L., Wang, L., Zhou, Q., Wang, H.: 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)

    Article  Google Scholar 

  23. Liu, Y.J., 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)

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang, T., Xia, M., Yi, Y., Shen, Q.: Adaptive neural dynamic surface control of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 2378–2387 (2017)

    Article  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Jiang, Z.P., Praly, L.: Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties. Automatica 34(7), 825–840 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ge, S.S., Hang, C.C., Zhang, T.: Adaptive neural network control of nonlinear systems by state and output feedback. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 29(6), 818–828 (1999)

    Article  Google Scholar 

  28. Liu, Y.J., Li, J., Tong, S., Chen, C.P.: Neural network control-based adaptive learning design for nonlinear systems with full-state constraints. IEEE Trans. Neural Netw. Learn. Syst. 27(7), 1562–1571 (2016)

    Article  MathSciNet  Google Scholar 

  29. Wang, H., Shi, P., Li, H., Zhou, Q.: Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Trans. Cybern. 47(10), 3075–3087 (2017)

    Article  Google Scholar 

  30. Carroll, J.J., Dawson, D.M.: Integrator backstepping techniques for the tracking control of permanent magnet brush DC motors. IEEE Trans. Ind. Appl. 31(2), 248–255 (1995)

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61773097, U1813214) and the Fundamental Research Funds for the Central Universities (No. N160402004).

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Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, People’s Republic of China

    Dan Ye, Yujin Cai & Haijiao Yang

  2. State Key Laboratory of Robotics, Shenyang Institute of Automation, CAS, Shenyang, 110016, People’s Republic of China

    Xingang Zhao

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  1. Dan Ye
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  2. Yujin Cai
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  3. Haijiao Yang
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  4. Xingang Zhao
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Correspondence to Xingang Zhao.

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Ye, D., Cai, Y., Yang, H. et al. Adaptive neural-based control for non-strict feedback systems with full-state constraints and unmodeled dynamics. Nonlinear Dyn 97, 715–732 (2019). https://doi.org/10.1007/s11071-019-05008-3

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  • DOI: https://doi.org/10.1007/s11071-019-05008-3

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