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Event-triggered neuroadaptive output-feedback control for nonstrict-feedback nonlinear systems with given performance specifications

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Abstract

This paper focuses on the event-triggered neuroadaptive output-feedback tracking control issue for nonstrict-feedback nonlinear systems with given performance specifications. By constructing a neural observer to estimate unmeasurable states, a novel event-triggered controller is presented together with a piecewise threshold rule. The presented event-triggered mechanism has two thresholds to reduce communication resources between the controller and actuator. The salient features of the presented controller are fourfold: (1) The tracking error can converge to a preassigned small region at predesigned converging mode within prescribed time, and the prescribed time is independent of initial conditions of system. (2) The strict constraint on the initial value of tracking error is relaxed largely via an improved speed function. (3) The complexity of our control algorithm can be reduced since there is no control signal in the trigger condition. (4) Command-filtered technology with filtering error compensating signal is applied to address the “explosion of complexity” problem. Furthermore, Lyapunov stability analysis demonstrates that under the presented event-triggered controller, all signals in the closed-loop system are semiglobally bounded, and the Zeno behavior is ruled out strictly. Numerical simulations are finally provided to illustrate the presented control scheme.

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References

  1. Zerari, N., Chemachema, M.: Event-triggered adaptive output-feedback neural-networks control for saturated strict-feedback nonlinear systems in the presence of external disturbance. Nonlinear Dyn. 4, 1343–1362 (2021)

    Google Scholar 

  2. Wang, L.B., Wang, H.Q., Liu, P.X.: Adaptive fuzzy finite-time control of stochastic nonlinear systems with actuator faults. Nonlinear Dyn. 104, 523–536 (2021)

    Google Scholar 

  3. Zhou, X., Gao, C., Li, Z.G., Ouyang, X.Y., Wu, L.B.: 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 

  4. Zhao, L., Yu, J.P., Wang, Q.G.: Finite-time tracking control for nonlinear systems via adaptive neural output feedback and command filtered backstepping. IEEE Trans. Neural Netw. Learn. Syst. 32(4), 1474–1485 (2021)

    MathSciNet  Google Scholar 

  5. Sun, K.K., Liu, L., Qiu, J.B., 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 

  6. Zhu, Q., Liu, Y., Wen, G.: Adaptive neural network output feedback control for stochastic nonlinear systems with full state constraints. ISA Trans. 101, 60–68 (2020)

    Google Scholar 

  7. Liu, Y., Zhu, Q.: Event-triggered adaptive neural network control for stochastic nonlinear systems with state constraints and time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3105681

    Article  Google Scholar 

  8. Shahvali, M., Naghibi-Sistani, M.B., Askari, J.: Adaptive fault compensation control for nonlinear uncertain fractional-order systems: static and dynamic event generator approaches. J. Frankl. Inst. 358(12), 6074–6100 (2021)

    MathSciNet  MATH  Google Scholar 

  9. Yang, D., Hu, X., Liu, W.J., Guo, C.: Finite-time control design for course tracking of disturbed ships subject to input saturation. Int. J. Control (2020). https://doi.org/10.1080/00207179.2020.1856930

    Article  Google Scholar 

  10. Ertugrul, T., Adli, M.A., Salamci, M.U.: Model reference adaptive control design for helicopters using gain scheduled reference models. In: Proceedings of 17th International Carpathian Control Conference, pp. 194–203. IEEE (2016)

  11. Joo, M.G., Lee, J.S.: A class of hierarchical fuzzy systems with constraints on the fuzzy rules. IEEE Trans. Fuzzy Syst. 13(2), 194–203 (2005)

    Google Scholar 

  12. Wang, A.Q., Liu, L., Qiu, J.B., Feng, G.: Event-triggered adaptive fuzzy output-feedback control for nonstrict-feedback nonlinear systems with asymmetric output constraint. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2974775

    Article  Google Scholar 

  13. Zou, A.M., Hou, Z.G., Tan, M.: Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans. Fuzzy Syst. 16(4), 886–897 (2008)

    Google Scholar 

  14. Zhang, L.L., Yang, G.H.: Fault-estimation-based output-feedback adaptive FTC for uncertain nonlinear systems with actuator faults. IEEE Trans. Ind. Electron. 67(4), 3065–3075 (2020)

    Google Scholar 

  15. Chen, B., Liu, K., Liu, X., Shi, P., Lin, C., Zhang, H.: Approximation-based adaptive neural control design for a class of nonlinear systems. IEEE Trans. Cybern. 44(5), 610–619 (2014)

    Google Scholar 

  16. Chen, B., Lin, C., Liu, X.P., Liu, K.F.: Adaptive fuzzy tracking control for a class of MIMO nonlinear systems in nonstrict-feedback form. IEEE Trans. Cybern. 45(12), 2744–2755 (2015)

    Google Scholar 

  17. Wang, H., Liu, K., Liu, X., Chen, B., Lin, C.: Neural-based adaptive output-feedback control for a class of nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Cybern. 45(9), 1977–1987 (2015)

    Google Scholar 

  18. Chen, B., Zhang, H.G., 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 

  19. Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Sys. 24(6), 1441–1454 (2016)

    Google Scholar 

  20. Chen, B., Zhang, H.G., Liu, X.P., Lin, C.: Neural observer and adaptive neural control design for a class of nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4261–4271 (2018)

    Google Scholar 

  21. Li, Y.M., Shao, X.F., Tong, S.C.: Adaptive fuzzy prescribed performance control of nontriangular structure nonlinear systems. IEEE Trans. Fuzzy Syst. 28(10), 2416–2426 (2020)

    Google Scholar 

  22. Zhang, H.G., Liu, Y., Wang, Y.C.: Observer-based finite-time adaptive fuzzy control for nontriangular nonlinear systems with full-state constraints. IEEE Trans. Cybern. 51(3), 1110–1120 (2021)

    Google Scholar 

  23. Zhou, Q., Li, H., Wang, L., Lu, R.: Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1747–1758 (2018)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  25. Li, Y., Tong, S., Liu, L., Feng, G.: Adaptive output-feedback control design with prescribed performance for switched nonlinear systems. Automatica 80, 225–231 (2017)

    MathSciNet  MATH  Google Scholar 

  26. Sui, S., Chen, C.L.P., Tong, S.: Neural network filtering control design for nontriangular structure switched nonlinear systems in finite time. IEEE Trans. Neural Netw. Learn. Syst. 30(7), 2153–2162 (2019)

    MathSciNet  Google Scholar 

  27. Sui, S., Tong, S., Chen, C.L.P.: Finite-time filter decentralized control for nonstrict-feedback nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 26(6), 3289–3300 (2018)

    Google Scholar 

  28. Zhao, Z., Jiang, Z.: Finite-time output feedback stabilization of lower-triangular nonlinear systems. Automatica 96, 259–269 (2018)

    MathSciNet  MATH  Google Scholar 

  29. Shahvali, M., Naghibi-Sistani, M.B., Askari, J.: Adaptive output-feedback bipartite consensus for nonstrict-feedback nonlinear multi-agent systems: a finite-time approach. Neurocomputing 318, 7–17 (2018)

    Google Scholar 

  30. Cui, G., Yu, J., Wang, Q.G.: Finite-time adaptive fuzzy control for MIMO nonlinear systems with input saturation via improved command-filtered backstepping. IEEE Trans. Syst. Man Cybern. Syst. 12, 12 (2020). https://doi.org/10.1109/TSMC.2020.3010642

    Article  Google Scholar 

  31. Ma, J., Ju, H.P., Xu, S.: Command-filter-based finite-time adaptive control for nonlinear systems with quantized input. IEEE Trans. Autom. Control 66(5), 2339–2344 (2021)

    MathSciNet  MATH  Google Scholar 

  32. Cui, G., Yu, J., Shi, P.: Observer-based finite-time adaptive fuzzy control with prescribed performance for nonstrict-feedback nonlinear systems. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.3048518

    Article  Google Scholar 

  33. Zhao, K., Song, Y.D., Ma, T.D., He, L.: Prescribed performance control of uncertain Euler–Lagrange systems subject to full-state constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3478–3489 (2018)

    MathSciNet  Google Scholar 

  34. Song, Y.D., Zhou, S.Y.: Neuroadaptive control with given performance specifications for MIMO strict-feedback systems under nonsmooth actuation and output constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4414–4425 (2018)

    Google Scholar 

  35. Liu, C.., G., C., Liu, X., Wang, H., Zhou, Y.: Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients. Nonlinear Dyn. 104, 3655–3670 (2021)

    Google Scholar 

  36. Qiu, J.B., Wang, T., Sun, K.K., Rudas, I.J., Gao, H.J.: Disturbance observer-based adaptive fuzzy control for strict-feedback nonlinear systems with finite-time prescribed performance. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3053327

    Article  Google Scholar 

  37. Sun, W., Wu, Y.Q., Sun, Z.Y.: Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 28(12), 3161–3170 (2020)

    Google Scholar 

  38. Liu, Y., Liu, X.P., Jing, Y.W., Zhang, Z.Y.: A novel finite-time adaptive fuzzy tracking control scheme for nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(4), 646–658 (2019)

    Google Scholar 

  39. Zhao, N., Shi, P., Xing, W., Chambers, J.: Observer-based event-triggered approach for stochastic networked control systems under denial of service attacks. IEEE Trans. Contr. Neural Netw. Syst. 8(1), 158–167 (2021)

    MathSciNet  Google Scholar 

  40. Qiu, J.B., Sun, K.K., Wang, T., Gao, H.J.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 27(11), 2152–2162 (2019)

    Google Scholar 

  41. Zhang, C.H., Yang, G.H.: Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures. IEEE Trans. Cybern. 50(1), 201–210 (2020)

    Google Scholar 

  42. Si, H., Shao, X., Zhang, W.: Fuzzy rule-based neural appointed-time control for uncertain nonlinear systems with aperiodic samplings. Expert Syst. Appl. 170(15), 114504 (2021)

    Google Scholar 

  43. Si, H., Shao, X., Zhang, W.: Event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors. Neural Comput. Appl. 33, 5771–5791 (2021)

    Google Scholar 

  44. Ma, J.L., Xu, S.Y., Ma, Q., Zhang, Z.Q.: Event-triggered adaptive neural network control for nonstrict-feedback nonlinear time-delay systems with unknown control directions. IEEE Trans. Neural Netw. Learn. Syst. 31(10), 4196–4205 (2020)

    MathSciNet  Google Scholar 

  45. Nai, Y.Q., Yang, Q.Y., Wu, Z.Z.: Prescribed performance adaptive neural compensation control for intermittent actuator faults by state and output feedback. IEEE Trans. Neural Netw. Learn. Syst. (2020). https://doi.org/10.1109/TNNLS.2020.3026208

    Article  Google Scholar 

  46. Xing, L., Wen, C., Liu, Z., Sun, H., Cai, J.: Adaptive compensation for actuator failures with event-triggered input. Automatica 85, 129–136 (2017)

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  48. Zhang, L.. L.., Yang, G..H.: Adaptive fuzzy prescribed performance control of nonlinear systems with hysteretic actuator nonlinearity and faults. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1747–1758 (2018)

    Google Scholar 

  49. Tong, S.C., Li, Y.M.: Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749–1764 (2009)

    MathSciNet  MATH  Google Scholar 

  50. Liu, Y.J., Gong, M.Z., Tong, S.C., Chen, C.L.P., Li, D.J.: Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints. IEEE Trans. Fuzzy Syst. 26(5), 2607–2617 (2018)

    Google Scholar 

  51. Liu, Y.J., Gong, M.Z., Liu, L., Tong, S.C., Chen, C.L.P.: Fuzzy observer constraint based on adaptive control for uncertain nonlinear MIMO systems with time-varying state constraints. IEEE Trans. Cybern. 51(3), 1308–1389 (2021)

    Google Scholar 

  52. Khalil, H., Praly, L.: High-gain observers in nonlinear feedback control. Int. J. Robust Nonlinear Control 24(6), 249–268 (2007)

    MathSciNet  MATH  Google Scholar 

  53. Yu, J., Zhao, L., Yu, H., Lin, C.: Barrier Lyapunov functions-based command filtered output feedback control for full-state constrained nonlinear systems. Automatica 105, 71–79 (2019)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  55. Sun, W., Su, S.F., Xia, J.W., Zhuang, G.M.: Command filter-based adaptive prescribed performance tracking control for stochastic uncertain nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. (2020). https://doi.org/10.1109/TSMC.2019.2963220

    Article  Google Scholar 

  56. 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)

    MathSciNet  MATH  Google Scholar 

  57. Zheng, Z.W., Feroskhan, M.: Path following of a surface vessel with prescribed performance in the presence of input saturation and external disturbances. IEEE/ASME Trans. Mechatron. 22(6), 2564–2575 (2017)

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (51879027, 51579024).

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Correspondence to Weijun Liu.

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Yang, D., Liu, W. & Guo, C. Event-triggered neuroadaptive output-feedback control for nonstrict-feedback nonlinear systems with given performance specifications. Nonlinear Dyn 107, 3593–3610 (2022). https://doi.org/10.1007/s11071-021-07161-0

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