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Nonlinear disturbance observer-based backstepping finite-time sliding mode tracking control of underwater vehicles with system uncertainties and external disturbances

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Abstract

In this paper, a nonlinear disturbance observer-based backstepping finite-time sliding mode control scheme for trajectory tracking of underwater vehicles subject to unknown system uncertainties and time-varying external disturbances is proposed. To reduce the influence of the uncertainties and external disturbances, a nonlinear disturbance observer is developed without any acceleration measurements to identify the lumped disturbance term. Additionally, the finite-time trajectory tracking controller is designed by combining second-order sliding mode control and backstepping design technique with the nonlinear disturbance observer. The finite-time convergence of motion tracking errors and the stability of the overall closed-loop control system are guaranteed by the Lyapunov approach. Besides, comprehensive simulation studies on trajectory tracking control of underwater vehicles are provided to demonstrate the effectiveness and performance of the proposed control scheme.

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References

  1. Kuipers, M., Ioannou, P.: Multiple model adaptive control with mixing. IEEE Trans. Autom. Control 55(8), 1822–1836 (2010)

    Article  MathSciNet  Google Scholar 

  2. Jiang, B., Gao, Z., Shi, P.: Adaptive fault-tolerant tracking control of near-space vehicle using Takagi–Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 18(5), 1000–1007 (2010)

    Article  Google Scholar 

  3. Peng, Z., Wang, D., Chen, Z.: Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics. IEEE Trans. Control Syst. Technol. 21(2), 513–520 (2013)

    Article  Google Scholar 

  4. Zhang, Y.P., Fidan, B., Loannou, P.A.: Backstepping control of linear time-varying systems with known and unknown parameters. IEEE Trans. Autom. Control 48(11), 1908–1925 (2003)

    Article  MathSciNet  Google Scholar 

  5. Antonelli, G., Chiaverini, S., Sarkar, N., West, M.: Adaptive control of an autonomous underwater vehicle: experimental results on ODIN. IEEE Trans. Control Syst. Technol. 9(5), 756–765 (2001)

    Article  Google Scholar 

  6. Antonelli, G., Caccavale, F., Chiaverini, S.: A novel adaptive control law for underwater vehicles. IEEE Trans. Control Syst. Technol. 11(2), 221–232 (2003)

    Article  Google Scholar 

  7. Yoerger, D.N., Slotine, J.E.: Robust trajectory control of underwater vehicles. IEEE J. Ocean. Eng. 10, 462–470 (1985)

    Article  Google Scholar 

  8. Goheen, K., Jefferys, E.: Multivariable self-tuning autopilots for autonomous and remotely operated underwater vehicles. IEEE J. Ocean. Eng. 15, 144–151 (1990)

    Article  Google Scholar 

  9. Healey, A.J., Lienard, D.: Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. IEEE J. Ocean. Eng. 18, 327–339 (1993)

    Article  Google Scholar 

  10. Lee, P.M., Hong, S.W., Lim, Y.K., Lee, C.M., Jeon, B.H., Park, J.W.: Discrete-time quasi-sliding mode control of an autonomous underwater vehicle. IEEE J. Ocean. Eng. 24, 388–395 (1999)

    Article  Google Scholar 

  11. McGookin, E.W.: Reconfigurable sliding mode control for submarine manoeuvring. In: Proceedings of the IEEE Oceans 01, pp. 1775–1782. Honolulu (2001)

  12. Silvestre, Carlos: A bottom-following preview controller for autonomous underwater vehicles. IEEE Trans. Control Syst. Technol. 17(2), 257–266 (2009)

    Article  Google Scholar 

  13. Yang, Y., Ren, J.: Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans. Fuzzy Syst. 11(6), 783–795 (2003)

    Article  Google Scholar 

  14. Chen, B., Liu, X.P., Tong, S.C.: Adaptive fuzzy output tracking control of mimo nonlinear uncertain systems. IEEE Trans. Fuzzy Syst. 15(2), 287–300 (2007)

    Article  Google Scholar 

  15. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern. A Syst. Hum. 40(1), 170–184 (2010)

    Article  Google Scholar 

  16. Gao, Q., Feng, G., Wang, Y., Qiu, J.: Universal fuzzy models and universal fuzzy controllers for stochastic non-affine nonlinear systems. IEEE Trans. Fuzzy Syst. 21(2), 328–341 (2013)

    Article  Google Scholar 

  17. Luo, W., Soares, C.G., Zou, Z.: Neural-network, \(L_2\)-gain-based cascaded control of underwater robot thrust. IEEE J. Ocean. Eng. 39, 630–640 (2014)

    Article  Google Scholar 

  18. Chen, M., Ge, S.S., How, B.V.E.: Robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities. IEEE Trans. Neural Netw. 21(5), 796–812 (2010)

    Article  Google Scholar 

  19. Liu, Y.J., Tong, S.C., Wang, D., Li, T.S., Chen, C.L.P.: Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear siso systems. IEEE Trans. Neural Netw. 22(8), 1328–1334 (2011)

    Article  Google Scholar 

  20. Polycarpou, M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447–451 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gao, Y., Er, M.J.: Design for self-organizing fuzzy neural networks based on genetic algorithms. IEEE Trans. Fuzzy Syst. 11(4), 462–477 (2003)

    Article  Google Scholar 

  22. Chen, C.S.: Robust self-organizing neural-fuzzy control with uncertainty observer for mimo nonlinear systems. IEEE Trans. Fuzzy Syst. 19(4), 694–706 (2011)

    Article  Google Scholar 

  23. Wang, N., Er, M.J., Meng, X.: A fast and accurate online selforganizing scheme for parsimonious fuzzy neural networks. Neurocomputing 72(16–18), 3818–3829 (2009)

    Article  Google Scholar 

  24. Wang, N., Er, M.J., Meng, X., Li, X.: An online self-organizing scheme for parsimonious and accurate fuzzy neural networks. Int. J. Neural Syst. 20(5), 389–403 (2010)

    Article  Google Scholar 

  25. Wang, N.: A generalized ellipsoidal basis function based online selfconstructing fuzzy neural network. Neural Process. Lett. 34(1), 13–37 (2011)

    Article  Google Scholar 

  26. Man, Z., Paplinskiand, A., Wu, H.: A robust MIMO terminal sliding mode control for rigid robotic manipulators. IEEE Trans. Autom. Control 39(12), 2464–2469 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  27. Feng, F., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  28. Perruquetti, W., Barbot, J.P.: Sliding Mode Control in Engineering. Marcel-Dekker, New York (2002)

    Book  Google Scholar 

  29. Edwards, C., Colet, E.F., Fridman, L.: Advances in variable structure and sliding mode control. Spfinger, Berlin (2006)

    Book  MATH  Google Scholar 

  30. Damiano, A., Gatto, G.L., Marongiu, I.: Second-order sliding mode control of DC drives. IEEE Trans. Ind. Electron. 51, 364–373 (2014)

    Article  Google Scholar 

  31. Taheri, B., Case, D., Richer, E.: Force and stiffness backstepping-sliding mode controller for pneumatic cylinders. IEEE Trans. Mechatron. 19(6), 1799–1809 (2014)

    Article  Google Scholar 

  32. Chen, W.H.: Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatron. 9(4), 706–710 (2004)

    Article  Google Scholar 

  33. Wu, J., Huang, J., Wang, Y., Xing, K.: Nonlinear disturbance observer-based dynamic surface control for trajectory tracking of pneumatic muscle system. IEEE Trans. Control Syst. Technol. 22(2), 440–455 (2014)

    Article  Google Scholar 

  34. Wei, X., Zhang, H., Guo, L.: Composite disturbance-observer-based control and terminal sliding mode control for uncertain structural systems. Int. J. Syst. Sci. 40(10), 1009–1017 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Yang, J., Li, S., Yu, X.: Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans. Ind. Electron. 60(1), 160–169 (2013)

    Article  Google Scholar 

  36. Bu, X.W., Wu, X.Y., Chen, Y.X., Bai, R.Y.: Design of a class of new nonlinear disturbance observers based on tracking differentiators for uncertain dynamic systems. Int. J. Control Autom. Syst. 13(3), 595–602 (2015)

    Article  Google Scholar 

  37. Bu, X., Wu, X., Zhang, R., Ma, Z., Huang, J.: Tracking differentiator design for the robust backstepping control of a flexible air-breathing hypersonic vehicle. J. Frankl. Inst. 352, 1739–1765 (2015)

    Article  MathSciNet  Google Scholar 

  38. Schoenwald, D.A.: Auvs: in space, air, water, and on the ground. IEEE Control Syst. Mag. 20, 15–18 (2000)

    Article  Google Scholar 

  39. Fossen, T.I.: Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Trondheim. Marine Cybernetics AS, Norway (2002)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  41. Feng, F., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  42. Choi, J.K., Kond, H.: On fault-tolerant control of a hovering AUV with four horizontal and two vertical thrusters. In: Proceedings of the IEEE Oceans 10. Sydney (2010)

  43. Bu, X., Wu, X., Huang, J.: A guaranteed transient performance-based adaptive neural control scheme with low-complexity computation for flexible air-breathing hypersonic vehicles. Nonlinear Dyn. 84, 2175–2194 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank Associate Editor and the reviewers for their very careful comments and helpful suggestions which improved this technical note significantly.

This work is supported by the National Natural Science Foundation of China (under Grants 51479018, 51379002 and 51009017) and Fundamental Research Funds for the Central Universities of China (under Grants 3132016335 and 3132016314).

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Correspondence to Siyuan Liu or Yancheng Liu.

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Liu, S., Liu, Y. & Wang, N. Nonlinear disturbance observer-based backstepping finite-time sliding mode tracking control of underwater vehicles with system uncertainties and external disturbances. Nonlinear Dyn 88, 465–476 (2017). https://doi.org/10.1007/s11071-016-3253-8

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