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Hierarchical sliding mode surface-based adaptive neural fault-tolerant control for switched nonlinear systems with average dwell time

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Abstract

This paper studies the adaptive neural fault-tolerant control (FTC) problem of a class of switched nonstrict-feedback nonlinear systems (NFNSs) via adopting the hierarchical sliding mode control (HSMC) method and the average dwell time (ADT) switching strategy. First, the original system is transformed into a new system with unknown compound nonlinear functions. Then, by utilizing the robust approximation capability of neural networks (NNs), the compound nonlinear functions are identified online. Furthermore, a novel hierarchical sliding mode surface-based adaptive neural fault-tolerant controller is designed, in which the denominator singular issue is successfully handled by using a modified projection algorithm. By means of the Lyapunov stability theory, it is proved that the proposed control method can ensure the boundedness of all signals of the considered NFNS. Eventually, a practical continuous stirred tank reactor example is given to verify the validity of the proposed HSMS-based adaptive neural FTC method.

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References

  1. 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. Cybernet. 49(7), 2536–2545 (2018)

    Google Scholar 

  2. Wang, H., Bai, W., Zhao, X., Liu, P.X.: Finite-time-prescribed performance-based adaptive fuzzy control for strict-feedback nonlinear systems with dynamic uncertainty and actuator faults. IEEE Trans. Cybernet. 52(7), 6959–6971 (2021)

    Google Scholar 

  3. Parsa, P., Akbarzadeh-T, M.R., Baghbani, F.: Command-filtered backstepping robust adaptive emotional control of strict-feedback nonlinear systems with mismatched uncertainties. Inf. Sci. 579, 434–453 (2021)

    MathSciNet  Google Scholar 

  4. Mahdy, A.: A numerical method for solving the nonlinear equations of Emden-fowler models. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.04.019

    Article  Google Scholar 

  5. Huang, S., Zong, G., Wang, H., Zhao, X., Alharbi, K.: Command Filter-Based Adaptive Fuzzy Self-Triggered Control for MIMO Nonlinear Systems with Time-Varying Full-State Constraints. Int. J. Fuzzy Syst. (2023). https://doi.org/10.1007/s40815-023-01560-8

    Article  Google Scholar 

  6. Zhao, Y., Niu, B., Zong, G., Zhao, X., Alharbi, K.: Neural network-based adaptive optimal containment control for non-affine nonlinear multi-agent systems within an identifier-actor-critic framework. J. Franklin Inst. 360(12), 8118–8143 (2023)

    MathSciNet  MATH  Google Scholar 

  7. Mahdy, A.M., Lotfy, K., El-Bary, A.: Use of optimal control in studying the dynamical behaviors of fractional financial awareness models. Soft Comput. 26(7), 3401–3409 (2022)

    Google Scholar 

  8. Zhao, Y., Zhang, H., Chen, Z., Wang, H., Zhao, X.: Adaptive neural decentralised control for switched interconnected nonlinear systems with backlash-like hysteresis and output constraints. Int. J. Syst. Sci. 53(7), 1545–1561 (2022)

    MathSciNet  MATH  Google Scholar 

  9. Xu, N., Chen, Z., Niu, B., Zhao, X.: Event-triggered distributed consensus tracking for nonlinear multi-agent systems: a minimal approximation approach. IEEE J. Emerg. Select. Top. Circuits Syst. (2023). https://doi.org/10.1109/JETCAS.2023.3277544

    Article  Google Scholar 

  10. Sun, Y., Gao, C., Wu, L.B., Yang, Y.H.: Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology. Nonlinear Dyn. 111(9), 8329–8345 (2023)

    Google Scholar 

  11. Wu, W., Xu, N., Niu, B., Zhao, X., Ahmad, A.: Low-Computation Adaptive Saturated Self-Triggered Tracking Control of Uncertain Networked Systems. Electronics. 12(13), 2771 (2023)

    Google Scholar 

  12. Mahdy, A.M.: Stability, existence, and uniqueness for solving fractional glioblastoma multiforme using a caputo-fabrizio derivative. Math. Methods Appl. Sci. (2023). https://doi.org/10.1002/mma.9038

    Article  Google Scholar 

  13. Li, Y., Tong, S.: Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans. Cybernet. 47(4), 1007–1016 (2016)

    Google Scholar 

  14. Cheng, F., Wang, H., Zhang, L., Ahmad, A., Xu, N.: Decentralized adaptive neural two-bit-triggered control for nonstrict-feedback nonlinear systems with actuator failures. Neurocomputing 500, 856–867 (2022)

    Google Scholar 

  15. Wu, T., Yu, Z., Li, S.: Observer-based adaptive fuzzy quantized fault tolerant control of nonstrict-feedback nonlinear systems with sensor fault. IEEE Trans. Fuzzy Syst. 31(6), 1900–1911 (2023)

    Google Scholar 

  16. Li, Y., Wang, H., Zhao, X., Xu, N.: Event-triggered adaptive tracking control for uncertain fractional-order nonstrict-feedback nonlinear systems via command filtering. Int. J. Robust Nonlinear Control 32(14), 7987–8011 (2022)

    MathSciNet  Google Scholar 

  17. Zhao, H., Wang, H., Xu, N., Zhao, X., Sharaf, S.: Fuzzy approximation-based optimal consensus control for nonlinear multiagent systems via adaptive dynamic programming. Neurocomputing. 533, 126529 (2023)

    Google Scholar 

  18. Tang, F., Wang, H., Zhang, L., Xu, N., Ahmad, A.: Adaptive optimized consensus control for a class of nonlinear multi-agent systems with asymmetric input saturation constraints and hybrid faults. Commun. Nonlinear Sci. Numer. Simul. 126, 107446 (2023)

  19. Zhang, J., Niu, B., Wang, D., Wang, H., Duan, P., Zong, G.: Adaptive neural control of nonlinear nonstrict feedback systems with full-state constraints: a novel nonlinear mapping method. IEEE Trans. Neural Netw. Learn. Syst. 34(2), 999–1007 (2023)

    MathSciNet  Google Scholar 

  20. Sui, S., Xu, H., Chen, C.P., Tong, S.: Non-singular fixed-time control of non-strict feedback mimo nonlinear system with asymptotically convergent tracking error. IEEE Trans. Fuzzy Syst. 31(5), 1689–1702 (2023)

    Google Scholar 

  21. Zhao, X., Wang, X., Ma, L., Zong, G.: Fuzzy approximation based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Trans. Fuzzy Syst. 28(4), 632–644 (2019)

    Google Scholar 

  22. Tang, F., Niu, B., Wang, H., Zhang, L., Zhao, X.: Adaptive fuzzy tracking control of switched mimo nonlinear systems with full state constraints and unknown control directions. IEEE Trans. Circuits Syst. II Express Briefs 69(6), 2912–2916 (2022)

    Google Scholar 

  23. Zhang, H., Zhao, X., Zhang, L., Niu, B., Zong, G., Xu, N.: Observer-based adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with input quantization. Int. J. Robust Nonlinear Control 32(14), 8163–8185 (2022)

    MathSciNet  Google Scholar 

  24. Guo, S., Zhao, X., Wang, H., Xu, N.: Distributed consensus of heterogeneous switched nonlinear multiagent systems with input quantization and dos attacks. Appl. Math. Comput. 456, 128127 (2023)

    MathSciNet  MATH  Google Scholar 

  25. Chen, H., Lim, C., Shi, P.: Robust-based control for uncertain stochastic fuzzy switched time-delay systems via integral sliding mode strategy. IEEE Trans. Fuzzy Syst. 30(2), 382–396 (2022)

    Google Scholar 

  26. Huo, X., Ma, L., Zhao, X., Zong, G.: Event-triggered adaptive fuzzy output feedback control of mimo switched nonlinear systems with average dwell time. Appl. Math. Comput. 365, 124665 (2020)

    MathSciNet  MATH  Google Scholar 

  27. Zhao, X.Q., Guo, S., Long, Y., Zhong, G.X.: Simultaneous fault detection and control for discrete-time switched systems under relaxed persistent dwell time switching. Appl. Math. Comput. 412, 126585 (2022)

    MathSciNet  MATH  Google Scholar 

  28. Chen, Y., Lazar, M.: An efficient mpc algorithm for switched systems with minimum dwell time constraints. Automatica 143, 110453 (2022)

    MathSciNet  MATH  Google Scholar 

  29. Zeng, D., Liu, Z., Chen, C.P., Zhang, Y., Wu, Z.: Adaptive fuzzy output-feedback predefined-time control of nonlinear switched systems with admissible edge-dependent average dwell time. IEEE Trans. Fuzzy Syst. 30(12), 5337–5350 (2022)

    Google Scholar 

  30. Nojoumian, M.A., Zakerzadeh, M.R., Ayati, M.: Stabilization of delayed switched positive nonlinear systems under mode dependent average dwell time: a bumpless control scheme. Nonlinear Anal. Hybrid Syst. 47, 101300 (2023)

    MathSciNet  MATH  Google Scholar 

  31. Cao, X., Zhang, C., Zhao, D., Li, Y.: Guaranteed cost positive consensus for multi-agent systems with multiple time-varying delays and mdadt switching. Nonlinear Dyn. 107(4), 3557–3572 (2022)

    Google Scholar 

  32. Liu, L., Cui, Y., Liu, Y.J., Tong, S.: Observer-based adaptive neural output feedback constraint controller design for switched systems under average dwell time. IEEE Trans. Circuits Syst. I Regular Papers 68(9), 3901–3912 (2021)

    Google Scholar 

  33. Gunasekaran, N., Ali, M.S., Arik, S., Ghaffar, H.A., Diab, A.A.Z.: Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal. Neural Netw. 149, 137–145 (2022)

    MATH  Google Scholar 

  34. Zhang, H., Wang, H., Niu, B., Zhang, L., Ahmad, A.M.: Sliding-mode surface-based adaptive actor-critic optimal control for switched nonlinear systems with average dwell time. Inf. Sci. 580, 756–774 (2021)

    MathSciNet  Google Scholar 

  35. Wang, T., Wang, H., Xu, N., Zhang, L., Alharbi, K.H.: Sliding-mode surface-based decentralized event-triggered control of partially unknown interconnected nonlinear systems via reinforcement learning. Inf. Sci. 641, 119070 (2023)

    Google Scholar 

  36. Zhang, Z., Guo, Y., Gong, D., Liu, J.: Global integral sliding-mode control with improved nonlinear extended state observer for rotary tracking of a hydraulic roofbolter. IEEE/ASME Trans. Mechatron. 28(1), 483–494 (2022)

    Google Scholar 

  37. Mobayen, S., Bayat, F., ud Din, S., Vu, M.T.: Barrier function-based adaptive nonsingular terminal sliding mode control technique for a class of disturbed nonlinear systems. ISA Trans. 134, 481–496 (2023)

    Google Scholar 

  38. Zhang, H., Zhao, X., Wang, H., Zong, G., Xu, N.: Hierarchical sliding-mode surface-based adaptive actor-critic optimal control for switched nonlinear systems with unknown perturbation. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3183991

    Article  Google Scholar 

  39. Yue, S., Niu, B., Wang, H., Zhang, L., Ahmad, A.: Hierarchical sliding mode-based adaptive fuzzy control for uncertain switched under-actuated nonlinear systems with input saturation and dead-zone. Rob. Intell. Autom. 43(5), 523–536

  40. Zhang, X., Zhang, L., Zhao, X., Zhao, N.: Reachable set control for singular systems with disturbance via sliding mode control. J. Frankl. Inst. 360(4), 3307–3329 (2023)

    MathSciNet  MATH  Google Scholar 

  41. Zhao, H., Zong, G., Zhao, X., Wang, H., Xu, N., Zhao, N.: Hierarchical Sliding-Mode Surface-Based Adaptive Critic Tracking Control for Nonlinear Multiplayer Zero-Sum Games via Generalized Fuzzy Hyperbolic Models. IEEE Transactions on Fuzzy Systems.(2023). https://doi.org/10.1109/TFUZZ.2023.3273566

  42. Zhang, H., Xu, N., Zong, G., Alkhateeb, A.F.: Adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with actuator faults. Int. J. Syst. Sci. 52(8), 1499–1514 (2021)

    MathSciNet  MATH  Google Scholar 

  43. Wang, X., Zhou, Y., Huang, T., Chakrabarti, P.: Event-triggered adaptive fault-tolerant control for a class of nonlinear multiagent systems with sensor and actuator faults. IEEE Trans. Circuits Syst. I Regular Papers 69(10), 4203–4214 (2022)

    Google Scholar 

  44. Zhao, Y., Wang, H., Xu, N., Zong, G., Zhao, X.: Reinforcement learning-based decentralized fault tolerant control for constrained interconnected nonlinear systems. Chaos, Solitons & Fractals 167, 113034 (2023)

    MathSciNet  Google Scholar 

  45. Wei, Q., Li, H., Li, T., Wang, F.Y.: A novel data-based fault-tolerant control method for multicontroller linear systems via distributed policy iteration. IEEE Trans. Syst. Man Cybernet. Syst. 53(5), 3176–3186 (2023)

  46. 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 (2020)

    Google Scholar 

  47. Ma, L., Xu, N., Zhao, X., Zong, G., Huo, X.: Small-gain technique-based adaptive neural output-feedback fault-tolerant control of switched nonlinear systems with unmodeled dynamics. IEEE Trans. Syst. Man Cybernet. Syst. 51(11), 7051–7062 (2020)

    Google Scholar 

  48. Guo, X., Xu, W., Wang, J., Park, J.: Distributed neuroadaptive fault-tolerant sliding-mode control for 2-d plane vehicular platoon systems with spacing constraints and unknown direction faults. Automatica 129, 109675 (2021)

    MathSciNet  MATH  Google Scholar 

  49. Zhang, H., Zhao, X., Zong, G., Xu, N.: Fully distributed consensus of switched heterogeneous nonlinear multi-agent systems with bouc-wen hysteresis input. IEEE Trans. Netw. Sci. Eng. 9(6), 4198–4208 (2022)

    MathSciNet  Google Scholar 

  50. Dipierro, S., Ros-Oton, X., Serra, J., Valdinoci, E.: Non-symmetric stable operators: regularity theory and integration by parts. Adv. Math. 401, 108321 (2022)

    MathSciNet  MATH  Google Scholar 

  51. Zhang, H., Zhao, X., Wang, H., Niu, B., Xu, N.: Adaptive tracking control for output-constrained switched mimo pure-feedback nonlinear systems with input saturation. J. Syst. Sci. Complex. 36(3), 960–984 (2023)

    MathSciNet  Google Scholar 

  52. Cheng, Y., Niu, B., Zhao, X., Zong, G., Ahmad, A.M.: Event-triggered adaptive decentralised control of interconnected nonlinear systems with bouc-wen hysteresis input. Int. J. Syst. Sci. 54(6), 1275–1288 (2023)

    MathSciNet  MATH  Google Scholar 

  53. Cao, Z., Niu, B., Zong, G., Zhao, X., Ahmad, A.M.: Active disturbance rejection-based event-triggered bipartite consensus control for nonaffine nonlinear multiagent systems. Int. J. Robust Nonlinear Control 33(12), 7181–7203 (2023)

    MathSciNet  Google Scholar 

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grants 62203064.

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Correspondence to Ning Xu.

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Xu, N., Niu, B., Zhang, H. et al. Hierarchical sliding mode surface-based adaptive neural fault-tolerant control for switched nonlinear systems with average dwell time. Nonlinear Dyn 111, 21747–21763 (2023). https://doi.org/10.1007/s11071-023-08990-x

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