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Event-triggered neural adaptive failure compensation control for stochastic systems with dead-zone output

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Abstract

This paper investigates event-triggered adaptive compensation control in the face of uncertain stochastic nonlinear system with actuator failure and output dead-zone. It is still an arduous task and challenge to design a compensation controller for uncertain stochastic nonlinear system. In order to avoid damaging output caused by the nonlinearity of the system, blended neural network integration with Nussbaum-type function is proposed. It is established to ensure the provision of the tracking error constraints, which is based on backstepping Lyapunov function technique. Additionally, system transmission resource constraints and actuator failure problems exist simultaneously in the system, which is extremely challenging for control design. More transmission resources are demanded when the system is suffered with actuator failures, while the system transmission resource is limited. Thus, the requirements cannot be achieved. It is difficult and challenged to ensure the system tracking performance. Using the proposed event-triggered controller and combining the Lyapunov synthesis, a novel optimization algorithm is deduced to guarantee the closed-loop system stability and the convergence of the tracking error. The simulation results illustrate the effectiveness of the proposed neural networks adaptive control approach.

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References

  1. Chen, C.L.P., Liu, Y.J., Wen, G.X.: Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems. IEEE Trans. Cybern. 44(5), 583–593 (2014)

    Article  Google Scholar 

  2. Chen, C.L.P., Wen, G.X., Liu, Y.J., Liu, Z.: Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semistrict-feedback multiagent systems. IEEE Trans. Cybern. 46(7), 1591–1601 (2016)

    Article  Google Scholar 

  3. Chen, B., Lin, C., Liu, X., Liu, K.: Observer-based adaptive fuzzy control for a class of nonlinear delayed systems. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 27–36 (2016)

    Article  Google Scholar 

  4. Chen, B., Liu, X., Liu, K., Lin, C.: Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans. Fuzzy Syst. 18(5), 883–892 (2010)

    Article  Google Scholar 

  5. Chen, B., Liu, X., Liu, K., Lin, C.: Novel adaptive neural control design for nonlinear MIMO time-delay systems. Automatica 45(6), 1554–1560 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cai, J., Wen, C., Su, H., Liu, Z.: Robust adaptive failure compensation of hysteretic actuators for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 58(9), 2388–2394 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cai, J.P., Wen, C.Y., Su, H.Y.: Adaptive inverse control for parametric strict feedback systems with unknown failures of hysteretic actuators. IEEE Int. J. Robust Nonlinear Control 25(6), 824–841 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fan, H., Liu, B., Shen, Y., Wang, W.: Adaptive failure compensation control for uncertain systems with stochastic actuator failures. IEEE Trans. Autom. Control 59(3), 808–814 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ge, S.S., Wang, C.: Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans. Neural Netw. 15(3), 674–692 (2004)

    Article  Google Scholar 

  10. Ge, Y., Wang, J., Zhang, L., Wang, B., Li, C.: Robust fault tolerant control of distributed networked control systems with variable structure. J. Franklin Inst. 353(12), 2553–2575 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Deng, H., Krsti, M.: Stochastic nonlinear stabilization i: a backstepping design. Syst. Control Lett. 32, 143–150 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)

    MATH  Google Scholar 

  13. Li, T.S., Wang, D., Feng, G., Tong, S.C.: A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man. Cybern. Part B (Cybern.) 40(3), 915–927 (2010)

    Article  Google Scholar 

  14. Lee, H.: Robust adaptive fuzzy control by backstepping for a class of MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 19(2), 265–275 (2011)

    Article  Google Scholar 

  15. Li, Y., Tong, S.: Adaptive fuzzy output-feedback control of purefeedback uncertain nonlinear systems with unknown dead zone. IEEE Trans. Fuzzy Syst. 22(5), 1341–1347 (2014)

    Article  Google Scholar 

  16. Lai, G., Liu, Z., Zhang, Y., Chen, C.L.P., Xie, S., Liu, Y.: Fuzzy adaptive inverse compensation method to tracking control of uncertain nonlinear systems with generalized actuator dead zone. IEEE Trans. Fuzzy Syst. 25(1), 191–204 (2017)

    Article  Google Scholar 

  17. 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 

  18. Li, Y.X., Yang, G.H.: Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems with actuator faults and unknown dead zones. IEEE Trans. Syst. Man. Cybern. Syst. 47(50), 729–740 (2017)

    Article  Google Scholar 

  19. Li, Y., Tong, S.: Adaptive neural networks decentralized FTC design for nonstrict-feedback nonlinear interconnected large-scale systems against actuator faults. IEEE Trans. Neural Netw. Learn. Syst. 28(11), 2541–2554 (2017)

    Article  MathSciNet  Google Scholar 

  20. Liu, S.J., Zhang, J.F., Jiang, Z.P.: Decentralized adaptive outputfeedback stabilization for large-scale stochastic nonlinear systems. Automatica 43, 238–251 (2007)

    Article  MathSciNet  Google Scholar 

  21. Polycarpou, M.M., Mears, M.J.: Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators. Int. J. Control 70(3), 363–384 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peng, C., Han, Q.L., Yue, D.: To transmit or not to transmit: a discrete event-triggered communication scheme for networked takagisugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 21, 164–170 (2013)

    Article  Google Scholar 

  23. Song, B., Hedrick, J.K.: Observer-based dynamic surface control for a class of nonlinear systems: an LMI approach. IEEE Trans. Autom. Control 49(11), 1995–2001 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. Song, B., Hedrick, J.K.: Robust stabilization and ultimate boundedness of dynamic surface control systems via convex optimization. IEEE Trans. Autom. Control 75(12), 870–881 (2002)

    MathSciNet  MATH  Google Scholar 

  25. Tong, S., Li, Y., Li, Y., Liu, Y.: Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans. Syst. Man. Cybern. Part B (Cybern.) 41(6), 1693–1704 (2011)

    Article  Google Scholar 

  26. 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 

  27. Tao, G., Joshi, S.M., Ma, X.: Adaptive state feedback and tracking control of systems with actuator failures. IEEE Trans. Autom. Control 46(1), 78–95 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Tao, G., Chen, S., Joshi, S.M.: An adaptive actuator failure compensation controller using output feedback. IEEE Trans. Autom. Control 47(3), 506–511 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  29. Tang, X., Tao, G., Joshi, S.M.: Adaptive output feedback actuator failure compensation for a class of nonlinear systems. Int. J. Adapt. Control Signal Process 19(6), 419–444 (2005)

    Article  MATH  Google Scholar 

  30. Tang, Y., Gao, H., Kurths, J.: Robust H1 self-triggered control of networked systems under packet dropouts. IEEE Trans. Cybern. 46, 3294–3305 (2016)

    Article  Google Scholar 

  31. Tong, S.C., Li, Y., Li, Y.M., Liu, Y.J.: Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans. Syst. 41, 1693–1704 (2011)

    Google Scholar 

  32. Tong, S., Li, Y.: Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21(1), 134–146 (2013)

    Article  Google Scholar 

  33. Tong, S., Wang, T., Li, Y.: Fuzzy adaptive actuator failure compensation control of uncertain stochastic nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. 22(3), 563–574 (2014)

    Article  Google Scholar 

  34. Tong, S.C., Li, Y., Li, Y.M., Liu, Y.J.: Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41, 1693–1704 (2011)

    Article  Google Scholar 

  35. Yi, Y., Zheng, W.X., Sun, C., Guo, L.: DOB fuzzy controller design for non-Gaussian stochastic distribution systems using two-step fuzzy identification. IEEE Trans. Fuzzy Syst. 24(2), 401–418 (2016)

    Article  Google Scholar 

  36. Yip, P.P., Hedrick, J.K.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71(5), 959–979 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  37. Yang, F., Zhang, H., Hui, G., Wang, S.: Mode-independent fuzzy fault-tolerant variable sampling stabilization of nonlinear networked systems with both time-varying and random delays. Fuzzy Sets Syst. 207, 45–63 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhai, D., An, L., Dong, J., Zhang, Q.: Simultaneous H2/H1 fault detection and control for networked systems with application to forging equipment. Signal Process. 125, 203–215 (2016)

    Article  Google Scholar 

  39. Zhang, Y., Peng, P.-Y., Jiang, Z.-P.: Stable neural controller design for unknown nonlinear systems using backstepping. IEEE Trans. Neural Netw. 11(6), 1347–1360 (2000)

    Article  Google Scholar 

  40. Zhang, T.P., Ge, S.S.: Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs. Automatica 43(6), 1021–1033 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44(7), 1895–1903 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang, M., Zhang, S., Chen, B., Luo, F.: Direct adaptive neural control for stabilization of nonlinear time-delay systems. Sci. China Inf. 53, 800–812 (2010)

    Article  MathSciNet  Google Scholar 

  43. Wang, Y.C., Zhang, H.G., Wang, Y.Z.: Fuzzy adaptive control of stochastic nonlinear systems with virtual control gain function. Acta Autom. Sin. 32, 170–178 (2006)

    MathSciNet  Google Scholar 

  44. Wu, D., Sun, X.M., Wen, C., Wang, W.: Redesigned predictive eventtriggered controller for networked control system with delays. IEEE Trans. Cybern. 46, 2195–2206 (2016)

    Article  Google Scholar 

  45. Wang, H., Liu, X., Liu, K.: Robust adaptive neural tracking control for a class of stochastic nonlinear interconnected systems. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 510–523 (2016)

    Article  MathSciNet  Google Scholar 

  46. Wang, H., Chen, B., Lin, C.: Adaptive neural control for strictfeedback stochastic nonlinear systems with time-delay. Neurocomputing 77(1), 267–274 (2012)

    Article  Google Scholar 

  47. Wang, M., Liu, X., Shi, P.: Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41(6), 1681–1692 (2011)

    Article  Google Scholar 

  48. Wang, X.S., Su, C.Y., Hong, H.H.: Robust adaptive control of a class of nonlinear systems with unknown dead-zone. Automatica 3, 407–413 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  49. Wang, W., Wen, C.: Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46(12), 2082–2091 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  50. Wang, C.L., Wen, C.Y., Lin, Y.: Decentralized adaptive backstepping control for a class of interconnected nonlinear systems with unknown actuator failures. IEEE J. Franklin Inst. 352(3), 835–850 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  51. Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, Bergen County, NJ (1994)

    Google Scholar 

  52. Wu, L., Yang, X., Lam, H.K.: Dissipativity analysis and synthesis for discrete-time t-s fuzzy stochastic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 22(2), 380–394 (2014)

    Article  Google Scholar 

  53. Wang, J., Liu, Z., Chen, C.L.P., Zhang, Y.: Fuzzy adaptive compensation control of uncertain stochastic nonlinear systems with actuator failures and input hysteresis. IEEE Trans. Cybern. 49(1), 2–13 (2019)

    Article  Google Scholar 

  54. Xie, X., Yue, D., Zhang, H., Peng, C.: Control synthesis of discretetime fuzzy systems: reducing the conservatism whilst alleviating the computational burden. IEEE Trans. Cybern. 47(9), 2480–2491 (2017)

    Article  Google Scholar 

  55. 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, 2071–2076 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for a number of constructive comments that have improved the presentation of this paper. This work was supported in part by the National Natural Science Foundation of China under Grant 61573108, in part by the Natural Science Foundation of Guangdong Province 2016A030313715, and in part by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme.

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Correspondence to Zhi Liu.

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Wang, J., Liu, Z., Chen, C.L.P. et al. Event-triggered neural adaptive failure compensation control for stochastic systems with dead-zone output. Nonlinear Dyn 96, 2179–2196 (2019). https://doi.org/10.1007/s11071-019-04916-8

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