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Nonlinear Dynamics

, Volume 95, Issue 1, pp 1–11 | Cite as

Decentralized low-complexity fault-tolerant tracking of a class of arbitrarily switched interconnected nonaffine nonlinear systems with unexpected faults

  • Sung Jin YooEmail author
Original Paper
  • 204 Downloads

Abstract

A low-complexity design strategy is proposed to ensure the decentralized fault-tolerant tracking quality of a class of uncertain switched interconnected nonaffine nonlinear systems. All system nonlinearities, nonlinear interaction faults, and actuator faults are arbitrarily switched and unknown. Compared with the existing decentralized tracking results, a universal decentralized tracking strategy is recursively provided to deal with asynchronously switched nonlinear interconnections and their faults, without requiring the signs of control coefficient functions and employing any fault compensators using adaptive nonlinear function approximators. Using the common Lyapunov function method, it is shown that the local tracking errors are maintained within preselected time-varying bounds regardless of arbitrary switched faults.

Keywords

Decentralized fault-tolerant tracking Low-complexity design Switched interaction faults Unknown control directions 

Notes

Acknowledgements

This research was supported by the Human Resources Development (No. 20174030201810) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy, by the Ministry of Science and ICT (MSIT), Korea, under the Information Technology Research Center (ITRC) support Program (IITP-2018-2014-0-00636) supervised by the Institute for Information and communications Technology Promotion (IITP) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03931312).

References

  1. 1.
    Jain, S., Khorrami, F.: Decentralized adaptive control of a class of large-scale interconnected nonlinear systems. IEEE Trans. Autom. Control 42(2), 136–154 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Wen, C.: Decentralized adaptive regulation. IEEE Trans. Autom. Control 39(10), 2163–2166 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Wang, C., Lin, Y.: Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems. Automatica 54, 16–24 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Yoo, S.J., Park, J.B., Choi, Y.H.: Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. Automatica 45, 436–443 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Zhang, Y., Wen, C., Soh, Y.C.: Robust decentralized adaptive stabilization of interconnected systems with guaranteed transient performance. Automatica 36, 907–915 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Zhang, X., Lin, Y.: Nonlinear decentralized control of large-scale systems with strong interconnections. Automatica 50, 2419–2423 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Yoo, S.J., Park, J.B.: Neural-network-based decentralized adaptive control for a class of large-scale nonlinear systems with unknown time-varying delays. IEEE Trans. Syst. Man Cybern. B Cybern. 39(5), 1316–1322 (2009)CrossRefGoogle Scholar
  8. 8.
    Li, Z.J., Yang, C.G., Su, C.-Y., Deng, S.M., Sun, F.C., Zhang, W.D.: Decentralized fuzzy control of multiple cooperating robotic manipulators with impedance interaction. IEEE Trans. Fuzzy Syst. 23(4), 1044–1056 (2015)CrossRefGoogle Scholar
  9. 9.
    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)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mehraeen, S., Jagannathan, S., Crow, M.L.: Decentralized dynamic surface control of large-scale interconnected systems in strict-feedback form using neural networks with asymptotic stabilization. IEEE Trans. Neural Netw. 22(11), 1709–1722 (2011)CrossRefGoogle Scholar
  11. 11.
    Li, Y., Tong, S., Li, T.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybernetics 45(1), 138–149 (2015)CrossRefGoogle Scholar
  12. 12.
    Hua, C., Guan, X.: Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans. Neural Netw. 19(4), 673–688 (2008)CrossRefGoogle Scholar
  13. 13.
    Tong, S., Liu, C.L., Li, Y.: Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties. IEEE Trans. Fuzzy Syst. 18(5), 845–861 (2010)CrossRefGoogle Scholar
  14. 14.
    Tong, S., Li, Y., Zhang, H.G.: Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays. IEEE Trans. Neural Netw. 22(7), 1073–1086 (2011)CrossRefGoogle Scholar
  15. 15.
    Tong, S., Li, Y.: Adaptive fuzzy decentralized output feedback control for nonlinear large-scale systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21(5), 913–925 (2013)CrossRefGoogle Scholar
  16. 16.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. Wiley, NJ (1995)zbMATHGoogle Scholar
  17. 17.
    Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Zhang, J.L., Gao, H.J.: Asynchronously switched control of switched linear systems with average dwell time. Automatica 46(5), 953–958 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Hou, Y., Tong, S.: Adaptive fuzzy output-feedback control for a class of nonlinear switched systems with unmodeled dynamics. Neurocomputing 168, 200–209 (2015)CrossRefGoogle Scholar
  20. 20.
    Tong, S., Sui, S., Li, Y.: Observed-based adaptive fuzzy tracking control for switched nonlinear systems with dead-zone. IEEE Trans. Cybernetics 45, 2816–2826 (2015)CrossRefGoogle Scholar
  21. 21.
    Zhang, L., Shi, P.: Stability, \(l_{2}\)-gain and asynchronous \(H_{\infty }\) control of discrete-time switched systems with average dwell time. IEEE Autom. Control 54(9), 2193–2200 (2009)Google Scholar
  22. 22.
    Zhang, L., Zhuang, S., Shi, P., Zhu, Y.: Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time. IEEE Autom. Control 60(11), 2994–2999 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Briat, C., Seuret, A.: Affine minimal and mode-dependent dwell-time characterization for uncertain switched linear systems. IEEE Trans. Autom. Control 58, 1304–1310 (2013)zbMATHCrossRefGoogle Scholar
  24. 24.
    Xu, X., Antsaklis, P.J.: Optimal control of switched systems based on parameterization of the switching instants. IEEE Trans. Autom. Control 49(1), 2–16 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Lian, J., Zhao, J.: Adaptive variable structure control for uncertain switched delay systems. Circuits, Syst. Signal Process. 29, 1089–1102 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Liberzon, D.: Switching in Systems and Control, Boston. Birkhauser, MA (2003)zbMATHCrossRefGoogle Scholar
  27. 27.
    Xiang, W., Xiao, J.: Stabilization of switched continuous-time systems with all modes unstable via dwell time switching. Automatica 50, 940–945 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Zhao, X., Zheng, X., Niu, B., Liu, L.: Adaptive tracking control for a class of uncertain switched nonlinear systems. Automatica 52, 185–191 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Jiang, B., Shen, Q., Shi, P.: Neural-networked adaptive tracking control for switched nonlinear pure-feedback systems under arbitrary switching. Automatica 61, 119–125 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Lee, S.W., Yoo, S.J.: Robust fault-tolerant prescribed performance tracking for uncertain switched pure-feedback nonlinear systems under arbitrary switching. Int. J. Syst. Sci. 48(3), 578–586 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Tong, S., Zhang, L., Li, Y.: Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead-zones. IEEE Trans. Systems, Man Cybern. Syst. 46(1), 37–47 (2016)CrossRefGoogle Scholar
  32. 32.
    Long, L.J., Zhao, J.: Decentralized adaptive fuzzy output-feedback control of switched large-scale nonlinear systems. IEEE Trans. Fuzzy Syst. 23(5), 1844–1860 (2015)CrossRefGoogle Scholar
  33. 33.
    Long, L.J., Zhao, J.: Decentralized adaptive neural output-feedback DSC for switched large-scale nonlinear systems. IEEE Trans. Cybern. 47(4), 908–919 (2017)CrossRefGoogle Scholar
  34. 34.
    Zhang, L., Yang, G.H.: Adaptive fuzzy output constrained decentralized control for switched nonlinear large-scale systems with unknown dead zones. Nonlinear Anal. Hybrid Syst. 23, 61–75 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Yoo, S.J.: Approximation-based decentralized adaptive tracking for a class of arbitrarily switched interconnected non-affine nonlinear systems. J. Franklin Inst. 354, 834–851 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Li, Y., Tong, S. (2018) Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. doi:  https://doi.org/10.1109/TNNLS.2017.2712698
  37. 37.
    Li, Y., Tong, S.: Fuzzy adaptive control design strategy of nonlinear switched large-scale systems. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2017.2703127
  38. 38.
    Bechlioulis, C.P., Rovithakis, G.A.: Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans. Autom. Control 53, 2090–2099 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Bechlioulis, C.P., Rovithakis, G.A.: Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. Automatica 45(2), 532–538 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Bechlioulis, C.P., Rovithakis, G.A.: A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems. Automatica 50, 1217–1226 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Wang, W., Wen, C.: Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica 46, 2082–2091 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Nussbaum, R.D.: Some remarks on a conjecture in parameter adaptive control. Syst. Control Lett. 3(5), 243–246 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Ge, S.S., Hong, F., Lee, T.H.: Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients. IEEE Trans. Syst. Man Cybern. B Cyber. 34(1), 499–516 (2004)CrossRefGoogle Scholar
  44. 44.
    Zhang, L., Yang, G.: Adaptive fuzzy output constrained decentralized control for switched nonlinear large-scale systems with unknown dead zones. Nonlinear Anal. Hybrid Syst. 23, 61–75 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Long, L., Zhao, J.: Decentralized adaptive neural output-feedback DSC for switched large-scale nonlinear systems. IEEE Trans. Cybern. 47(4), 908–919 (2017)CrossRefGoogle Scholar
  46. 46.
    Ge, S.S., Wang, C.: Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38, 671–682 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Wang, C., Hill, D.J., Ge, S.S., Ghen, G.: An ISS-modular approach for adaptive neural control of pure-feedback systems. Automatica 42, 723–731 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Zhang, T.P., Ge, S.S.: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica 44, 1895–1903 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Ryan, E.P.: A universal adaptive stabilizer for a class of nonlinear systems. Syst. Control Lett. 16, 209–218 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Jin, X., Wang, S., Qin, J., Zheng, W.X., Kang, Y.: Adaptive fault-tolerant consensus for a class of uncertain nonlinear second-order multi-agent systems with circuit implementation. IEEE Trans. Circuits Syst-I: Regul. Pap. 65(7), 2243–2255 (2018)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Jin, X.Z., He, Y.G., He, Y.G.: Finite-time robust fault-tolerant control against actuator faults and saturations. IET Control Theory Appl. 11(4), 550–556 (2017)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Jin, X., Qin, J., Shi, Y., Zheng, W.X.: Auxiliary fault tolerant control with actuator amplitude saturation and limited rate. IEEE Trans. Syst. Man Cybern. Syst. (2018).  https://doi.org/10.1109/TSMC.2017.2752961
  53. 53.
    Shi, L., Singh, S.K.: Decentralized adaptive controller design for large-scale systems with higher order interconnections. IEEE Trans. Autom. Control 37(8), 1106–1118 (1992)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Electrical and Electronics EngineeringChung-Ang UniversityDongjak-guRepublic of Korea

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