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Finite-time sliding mode fault-tolerant neural network control for nonstrict-feedback nonlinear systems

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Abstract

The article concentrates on the finite-time fault-tolerant control for a class of nonstrict-feedback nonlinear systems subject to uncertain control gains and multiple actuator faults. First, neural networks are employed to approximate system uncertainties. By means of a vital structural attribute of neural networks, algebraic loop problem in standard backstepping control design is excluded. Then, a sliding manifold with exponential monotonic attenuation is introduced to ensure chattering-free response and robust performance. Besides, the lumped uncertainty of multiple faulty actuators is handled via applying Nussbaum gain technique and a modified Nussbaum boundedness criterion. To circumvent the issue of “complexity explosion”, a second-order command filter is introduced in every step of recursive control design. Through the proposed adaptive finite-time fault-tolerant control scheme, the influence of actuator faults can be compensated effectively, and the tracking error converges into an arbitrarily small residuum in finite time. Meanwhile, the disc domain of convergent error as well as the upper bound of settling time can be estimated. Finally, two simulations concerned with practical models are discussed. It is expounded that the proposed scheme has more efficiency and less conservatism via comparing it with other existing methods.

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Availability of data and materials

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Li, Y., Yang, G.: Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults. Automatica 72, 177–185 (2016)

    MathSciNet  MATH  Google Scholar 

  2. Yu, Z., Li, Y., Lv, M., Chang, J., Pei, B.: Predefined-time anti-saturation fault-tolerant attitude control for tailless aircraft with guaranteed output constraints. Nonlinear Dyn. 111, 1399–1416 (2023)

    Google Scholar 

  3. Liu, H., Pan, Y., Cao, J., Wang, H., Zhou, Y.: Adaptive neural network backstepping control of fractional-order nonlinear systems with actuator faults. IEEE Trans. Neural Netw. Learn. Syst. 31(12), 5166–5177 (2020)

    MathSciNet  Google Scholar 

  4. Shen, Q., Jiang, B., Shi, P., Lim, C.-C.: Novel neural networks-based fault tolerant control scheme with fault alarm. IEEE Trans. Cybern. 44(11), 2190–2201 (2014)

    Google Scholar 

  5. Mushage, B.O., Chedjou, J.C., Kyamakya, K.: Observer-based fuzzy adaptive fault-tolerant nonlinear control for uncertain strict-feedback nonlinear systems with unknown control direction and its applications. Nonlinear Dyn. 88(4), 2553–2575 (2017)

    MATH  Google Scholar 

  6. Habibi, H., Nohooji, R.H., Howard, I.: Backstepping Nussbaum gain dynamic surface control for a class of input and state constrained systems with actuator faults. Inf. Sci. 482, 27–46 (2019)

    MathSciNet  MATH  Google Scholar 

  7. Meng, F., Zhao, L., Yu, J.: Backstepping based adaptive finite-time tracking control of manipulator systems with uncertain parameters and unknown backlash. J. Frank. Inst. 357(16), 11281–11297 (2020)

    MathSciNet  MATH  Google Scholar 

  8. Li, Y., Qu, F., Tong, S.: Observer-based fuzzy adaptive finite-time containment control of nonlinear multiagent systems with input delay. IEEE Trans. Cybern. 51(1), 126–137 (2021)

    Google Scholar 

  9. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control. Optim. 38(3), 751–766 (2000)

    MathSciNet  MATH  Google Scholar 

  10. Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)

    MathSciNet  MATH  Google Scholar 

  11. Zhu, Z., Xia, Y., Fu, M.: Attitude stabilization of rigid spacecraft with finite-time convergence. Int. J. Robust Nonlinear Control 21(6), 686–702 (2011)

    MathSciNet  MATH  Google Scholar 

  12. Sun, Y., Chen, B., Lin, C., Wang, H.: Finite-time adaptive control for a class of nonlinear systems with nonstrict feedback structure. IEEE Trans. Cybern. 48(10), 2774–2782 (2018)

    Google Scholar 

  13. Yu, J., Shi, P., Zhao, L.: Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica 92, 173–180 (2018)

    MathSciNet  MATH  Google Scholar 

  14. Sui, S., Chen, C.L.P., Tong, S.: Finite-time adaptive fuzzy prescribed performance control for high-order stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. 30(7), 2227–2240 (2022)

    Google Scholar 

  15. Li, S., Ahn, C.K., Xiang, Z.: Command-filter-based adaptive fuzzy finite-time control for switched nonlinear systems using state-dependent switching method. IEEE Trans. Fuzzy Syst. 29(4), 833–845 (2021)

    Google Scholar 

  16. Sun, K., Liu, L., Qiu, J., Feng, G.: Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 29(4), 786–796 (2021)

    Google Scholar 

  17. Cui, G., Yang, W., Yu, J.: Neural network-based finite-time adaptive tracking control of nonstrict-feedback nonlinear systems with actuator failures. Inf. Sci. 545, 298–311 (2021)

    MathSciNet  MATH  Google Scholar 

  18. Liu, L., Liu, Y., Tong, S.: Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems. IEEE Trans. Cybern. 49(7), 2536–2545 (2019)

    Google Scholar 

  19. Li, Y.: Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems. Automatica 106, 117–123 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Xue, G., Lin, F., Li, S., Liu, H.: Adaptive dynamic surface control for finite-time tracking of uncertain nonlinear systems with dead-zone inputs and actuator faults. Int. J. Control Autom. Syst. 19, 2797–2811 (2021)

    Google Scholar 

  21. Kamalamiri, A., Shahrokhi, M., Mohit, M.E.: Adaptive finite-time neural control of non-strict feedback systems subject to output constraint, unknown control direction, and input nonlinearities. Inf. Sci. 520, 271–291 (2020)

    MathSciNet  MATH  Google Scholar 

  22. Wang, H., Liu, P.X., Zhao, X., Liu, X.: Adaptive fuzzy finite-time control of nonlinear systems with actuator faults. IEEE Trans. Cybern. 50(5), 1786–1797 (2020)

    Google Scholar 

  23. Zhang, J., Tong, S., Li, Y.: Adaptive fuzzy finite-time output-feedback fault-tolerant control of nonstrict-feedback systems against actuator faults. IEEE Trans. Syst. Man Cybern.: Syst. 52(2), 1276–1287 (2022)

    Google Scholar 

  24. Xu, S.S.-D., Chen, C.-C., Wu, Z.-L.: Study of nonsingular fast terminal sliding-mode fault-tolerant control. IEEE Trans. Industr. Electron. 62(6), 3906–3913 (2015)

    Google Scholar 

  25. Ni, J., Liu, L., Tang, Y., Liu, C.: Predefined-time consensus tracking of second-order multiagent systems. IEEE Trans. Syst. Man Cybern.: Syst. 51(4), 2550–2560 (2021)

    Google Scholar 

  26. Yang, T., Deng, Y., Li, H., Sun, Z., Cao, H., Wei, Z.: Fast integral terminal sliding mode control with a novel disturbance observer based on iterative learning for speed control of PMSM. ISA Trans. 134, 460–471 (2023)

    Google Scholar 

  27. Zhang, M., Zang, H., Bai, L.: A new predefined-time sliding mode control scheme for synchronizing chaotic systems. Chaos Solitons Fractals 164, 112745 (2022)

    MathSciNet  MATH  Google Scholar 

  28. Song, J., Niu, Y., Zou, Y.: Finite-time stabilization via sliding mode control. IEEE Trans. Autom. Control 62(3), 1478–1483 (2017)

    MathSciNet  MATH  Google Scholar 

  29. Xue, G., Lin, F., Li, S., Liu, H.: Adaptive fuzzy finite-time backstepping control of fractional-order nonlinear systems with actuator faults via command-filtering and sliding mode technique. Inf. Sci. 600, 189–208 (2022)

    Google Scholar 

  30. Dong, W., Farrell, J.A., Polycarpou, M.M., Djapic, V., Sharma, M.: Command filtered adaptive backstepping. IEEE Trans. Control Syst. Technol. 20(3), 566–580 (2012)

    Google Scholar 

  31. Nussbaum, R.D.: Some remarks on a conjeture in parameter adaptive control. Syst. Control Lett. 3(5), 243–246 (1983)

    MATH  Google Scholar 

  32. Du, H., Shao, H., Yao, P.: Adaptive neural network control for a class of low-triangular-structured nonlinear systems. IEEE Trans. Neural Netw. 17(2), 509–514 (2006)

    Google Scholar 

  33. Zheng, Y., Wen, C., Li, Z.: Robust adaptive asymptotic tracking control of uncertain nonlinear systems subject to nonsmooth actuator nonlinearities. Int. J. Adapt. Control Signal Process. 27(1–2), 108–121 (2013)

    MathSciNet  MATH  Google Scholar 

  34. Psillakis, H.E.: Further results on the use of Nussbaum gains in adaptive neural network control. IEEE Trans. Autom. Control 55(12), 2841–2846 (2010)

    MathSciNet  MATH  Google Scholar 

  35. Farrell, J.A., Polycarpou, M.M.: Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches. Wiley, New York (2006)

    Google Scholar 

  36. Pan, Y., Sun, T., Liu, Y., Yu, H.: Composite learning from adaptive backstepping neural network control. Neural Netw. 95, 134–142 (2017)

    MATH  Google Scholar 

  37. Sun, Y., Chen, B., Lin, C., Wang, H., Zhou, S.: Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach. Inf. Sci. 369, 748–764 (2016)

    MATH  Google Scholar 

  38. Kurdila, A.J., Narcowich, F.J., Ward, J.D.: Persistency of excitation in identification using radial basis function approximants. SIAM J. Control. Optim. 33(2), 625–642 (1995)

    MathSciNet  MATH  Google Scholar 

  39. Yu, J., Shi, P., Dong, W., Yu, H.: Observer and command-filter-based adaptive fuzzy output feedback control of uncertain nonlinear systems. IEEE Trans. Industr. Electron. 62(9), 5962–5970 (2015)

    Google Scholar 

  40. Ginoya, D., Shendge, P.D., Phadke, S.B.: Disturbance observer based sliding mode control of nonlinear mismatched uncertain systems. Commun. Nonlinear Sci. Numer. Simul. 26(1–3), 98–107 (2015)

    MathSciNet  MATH  Google Scholar 

  41. Pan, Y., Yang, C., Pan, L., Yu, H.: Integral sliding mode control: Performance, modification, and improvement. IEEE Trans. Industr. Inf. 14(7), 3087–3096 (2018)

    Google Scholar 

  42. Wang, F., Wang, J., Wang, K., Zong, Q., Hua, C.: Adaptive backstepping sliding mode control of uncertain semi-strict nonlinear systems and application to permanent magnet synchronous motor. J. Syst. Sci. Complexity 34, 552–571 (2021)

  43. Wu, C., Liu, J., Xiong, Y., Wu, L.: Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems. IEEE Trans. Neural Netw. Learn. Syst. 29(7), 3022–3033 (2018)

    MathSciNet  Google Scholar 

  44. 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)

    Google Scholar 

  45. Chen, B., Zhang, H., Lin, C.: Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 89–98 (2016)

    MathSciNet  Google Scholar 

  46. Zhou, X., Gao, C., Li, Z., Ouyang, X., Wu, L.: Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation. Nonlinear Dyn. 103, 1645–1661 (2021)

    Google Scholar 

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Funding

This work was supported by Guangxi Natural Science Foundation (Grant Nos. 2023GXNSFAA026174, 2021GXNSFAA220114, 2022GXNSFAA035552, 2021GXNSFBA220033), the National Natural Science Foundation of China (Grant Nos. 61967001, 12261009), the Natural Science Basic Research Program of Shaanxi (Program No. 2023-JCQN-0008), the Middle-aged and Young Teachers’ Basic Ability Promotion Project of Guangxi (Grant No. 2023KY0680), Guangxi First-class Discipline Statistics Construction Project Fund (Grant No. TJYLXKDSJ2022B08), Guangxi University of Finance and Economics Land and Sea Economic Integration Collaborative Innovation Center (Grant No. 2022YB12), Guangxi Key Laboratory of Big Data in Finance and Economics (Grant No. FED2204), and Guangxi Colleges and Universities Key Laboratory of Quantitative Economics.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China

    Funing Lin & Shenggang Li

  2. School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning, 530003, China

    Funing Lin & Guangming Xue

  3. School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, China

    Heng Liu

  4. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China

    Yongping Pan

  5. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

Authors
  1. Funing Lin
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  2. Guangming Xue
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  3. Shenggang Li
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  4. Heng Liu
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  6. Jinde Cao
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Contributions

Conceptualization, formal analysis and investigation were performed by Funing Lin, Guangming Xue and Shenggang Li. Supervision, validation and visualization were performed by Heng Liu, Yongping Pan and Jinde Cao. Writing–original draft, methodology and software were performed by Funing Lin. Writing–review & editing and data curation were performed by Guangming Xue. Funding acquisition was performed by Funing Lin, Guangming Xue and Heng Liu. All authors have read and approved the final manuscript.

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Correspondence to Guangming Xue.

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Lin, F., Xue, G., Li, S. et al. Finite-time sliding mode fault-tolerant neural network control for nonstrict-feedback nonlinear systems. Nonlinear Dyn 111, 17205–17227 (2023). https://doi.org/10.1007/s11071-023-08767-2

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  • DOI: https://doi.org/10.1007/s11071-023-08767-2

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