Advertisement

Fixed-time Trajectory Tracking Control of a Full State Constrained Marine Surface Vehicle with Model Uncertainties and External Disturbances

  • Mingyu Fu
  • Taiqi WangEmail author
  • Chenglong Wang
Article
  • 36 Downloads

Abstract

This paper addresses the fixed-time trajectory tracking control problem of a fully actuated marine surface vehicle with full state constraints and system uncertainties. A continuous fixed-time convergence tracking controller is proposed based on fixed-time control and adding a power integrator methods, which achieves system stabilization within a finite time independent of system initial conditions. Moreover, a novel barrier Lyapunov function with a power integrator is designed to ensure the full state tracking error within the constraints. To accurately estimate the lumped disturbances of the vehicle system, a fixed-time disturbance observer is designed to guarantee the settling time of the disturbance observer bounded by a time constant independent of initial estimation errors. Finally, the proposed control scheme is proved to be fixed-time stable via fixed-time Lyapunov stability theorem and the full state constraints can never be violated. A numerical simulation is provided to illustrate the effectiveness and superiority of the proposed control scheme.

Keywords

Barrier Lyapunov function fixed-time control marine surface vehicle trajectory tracking. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G. Li, W. Li, H. P. Hildre, and H. Zhang, “Online learning control of surface vessels for fine trajectory tracking,” Journal of Marine Science and Technology, vol. 21, no. 2, pp. 251–260, June 2016.CrossRefGoogle Scholar
  2. [2]
    M. Breivik and T. I. Fossen, “Motion control concepts for trajectory tracking of fully actuated ships,” Proc. of the 7th IFAC Conference on Manoeuvring and Control of Marine Craft, 2006.Google Scholar
  3. [3]
    W. Xie, B. Ma, W. Huang, and Y. Zhao, “Global trajectory tracking control of underactuated surface vessels with nondiagonal inertial and damping matrices,” Nonlinear Dynamics, vol. 92, no. 4, pp. 1481–1492, June 2018.CrossRefzbMATHGoogle Scholar
  4. [4]
    R. Skjetne, T. I. Fossen, and P. V. Kokotovic, “Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory,” Automatica, vol. 41, pp. 289–298, February 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. Cheng, J. Yi, and D. Zhao, “Design of a sliding mode controller for trajectory tracking problem of marine vessels,” IET Control Theory and Applications, vol. 1, no. 1, pp. 233–237, January 2007.MathSciNetCrossRefGoogle Scholar
  6. [6]
    H. Ashrafiuon, K. R. Muske, L. C. McNinch, and R. A. Soltan, “Sliding-mode tracking control of surface vessels,” IEEE Trans. on Industrial Electronics, vol. 55, no. 11, pp. 4004–4012, November 2008.CrossRefGoogle Scholar
  7. [7]
    C. Liu, Z. Zou, and X. Hou, “Stabilization and tracking of underactuated surface vessels in random waves with fin based on adaptive hierarchical sliding mode technique,” Asian Journal of Control, vol. 16, no. 5, pp. 1492–1500, September 2014.CrossRefzbMATHGoogle Scholar
  8. [8]
    B. Chen, K. Liu, X. Liu, P. Shi, C. Lin, and H. Zhang, “Approximation-based adaptive neural control design for a class of nonlinear systems,” IEEE Trans. on Cybernetics, vol. 44, no. 5, pp. 610–619, May 2014.CrossRefGoogle Scholar
  9. [9]
    K. P. Tee and S. S. Ge, “Control of fully actuated ocean surface vessels using a class of feedforward approximators,” IEEE Trans. on Control Systems Technology, vol. 14, no. 4, pp. 750–756, July 2006.CrossRefGoogle Scholar
  10. [10]
    L. J. Zhang, H. Jia, and X. Qi, “NNFFC-adaptive output feedback trajectory tracking control for a surface ship at high speed,” Ocean Engineering, vol. 38, no. 13, pp. 1430–1438, September 2011.CrossRefGoogle Scholar
  11. [11]
    N. Wang and M. J. Er, “Self-constructing adaptive robust fuzzy neural tracking control of surface vehicles with uncertainties and unknown disturbances,” IEEE Trans. on Control Systems Technology, vol. 23, no. 3, pp. 991–1002, May 2015.CrossRefGoogle Scholar
  12. [12]
    B. S. Park, J. W. Kwon, and H. Kim, “Neural networkbased output feedback control for reference tracking of underactuated surface vessels,” Automatica, vol. 77, pp. 353–359, March 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Z. Yin, W. He, C. Yang, and C. Sun, “Control design of a marine vessel system using reinforcement learning,” Neurocomputing, vol. 311, pp. 353–362, October 2018.CrossRefGoogle Scholar
  14. [14]
    N. Wang and M. J. Er, “Direct adaptive fuzzy tracking control of marine vehicles with fully unknown parametric dynamics and uncertainties,” IEEE Trans. on Control Systems Technology, vol. 24, no. 5, pp. 1845–1852, September 2016.CrossRefGoogle Scholar
  15. [15]
    N. Wang, M. J. Er, J. C. Sun, and Y. C. Liu, “Adaptive robust online constructive fuzzy control of a complex surface vehicle system,” IEEE Trans. on Cybernetics, vol. 46, no. 7, pp. 1511–1523, July 2016.CrossRefGoogle Scholar
  16. [16]
    N. Wang, C. Qian, J. C. Sun, and Y. C. Liu, “Adaptive robust finite-time trajectory tracking control of fully actuated marine surface vehicles,” IEEE Trans. on Control Systems Technology, vol. 24, no. 4, pp. 1454–1462, July 2016.CrossRefGoogle Scholar
  17. [17]
    N. Wang, S. Lv, W. Zhang, Z. Liu, and M. J. Er, “Finitetime observer based accurate tracking control of a marine vehicle with complex unknowns,” Ocean Engineering, vol. 145, pp. 406–415, November 2017.CrossRefGoogle Scholar
  18. [18]
    N. Wang, S. Lv, M. J. Er, and W. H. Chen, “Fast and accurate trajectory tracking control of an autonomous surface vehicle with unmodeled dynamics and disturbances,” IEEE Trans. on Intelligent Vehicles, vol. 1, no. 3, pp. 230–243, September 2016.CrossRefGoogle Scholar
  19. [19]
    X. Huang, W. Lin, and B. Yang, “Global finite-time stabilization of a class of uncertain nonlinear systems,” Automatica, vol. 41, no. 5, pp. 881–888, May 2005.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    J. Li, C. Qian, and S. Ding, “Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems,” International Journal of Control, vol. 83, no. 11, pp. 2241–2252, September 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    F. Li and Y. Liu, “Global finite-time stabilization via timevarying output-feedback for uncertain nonlinear systems with unknown growth rate,” International Journal of Robust and Nonlinear Control, vol. 27, no. 17, pp. 4050–4070, November 2017.MathSciNetzbMATHGoogle Scholar
  22. [22]
    A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Trans. on Automatic Control, vol. 57, no. 8, pp. 2106–2110, August 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    L. Yuan, C. Li, B. Jiang, and G. Ma, “Fixed-time spacecraft attitude stabilization using homogeneous method,” Proc. of UKACC 11th International Conference on Control, 2016.Google Scholar
  24. [24]
    B. Tian, H. Lu, Z. Zuo, and H. Wang, “Fixed-time stabilization of high-order integrator systems with mismatched disturbances,” Nonlinear Dynamics, vol. 94, no. 4, pp. 2889–2899, December 2018.CrossRefGoogle Scholar
  25. [25]
    Z. Zuo, “Non-singular fixed-time terminal sliding mode control of non-linear systems,” IET Control Theory and Applications, vol. 9, no. 4, pp. 545–552, February 2015.MathSciNetCrossRefGoogle Scholar
  26. [26]
    J. Ni, L. Liu, C. Liu, X. Hu, and S. Li, “Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system,” IEEE Trans. on Circuits and Systems II: Express Briefs, vol. 64, no. 2, pp. 151–155, Feburary 2017.CrossRefGoogle Scholar
  27. [27]
    J. Li, Y. Yang, C. Hua, and X. Guan, “Fixed-time backstepping control design for high-order strict-feedback nonlinear systems via terminal sliding mode,” IET Control Theory and Applications, vol. 11, no. 8, pp. 1184–1193, May 2017.MathSciNetCrossRefGoogle Scholar
  28. [28]
    Z. Zhang and Y. Wu, “Fixed-time regulation control of uncertain nonholonomic systems and its applications,” International Journal of Control, vol. 90, no. 7, pp. 1327–1344, July 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Z. Zheng, M. Feroskhan, and L. Sun, “Adaptive fixed-time trajectory tracking control of a stratospheric airship,” ISA Transactions, vol. 76, pp. 134–144, May 2018.CrossRefGoogle Scholar
  30. [30]
    J. Ni, C. Liu, and H. Liu, “Continuous uniformly finite time exact disturbance observer based control for fixedtime stabilization of nonlinear systems with mismatched disturbances,” PLOS One, vol. 12, no. 4, April 2017.Google Scholar
  31. [31]
    K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, April 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    K. P. Tee and S. S. Ge, “Control of nonlinear systems with partial state constraints using a barrier Lyapunov function,” International Journal of Control, vol. 84, no. 12, pp. 2008–2023, November 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    C. Wang, Y. Wu, and J. Yu, “Barrier Lyapunov functionsbased adaptive control for nonlinear pure-feedback systems with time-varying full state constraints,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2714–2722, December 2017.CrossRefGoogle Scholar
  34. [34]
    Z. Zhao, W. He, and S. S. Ge, “Adaptive neural network control of a fully actuated marine surface vessel with multiple output constraints,” IEEE Trans. on Control Systems Technology, vol. 22, no. 4, pp. 1536–1543, July 2014.CrossRefGoogle Scholar
  35. [35]
    L. Kong, W. He, C. Yang, G. Li, and Z. Zhang, “Adaptive fuzzy control for a marine vessel with time-varying constraints,” IET Control Theory and Applications, vol. 12, no. 10, pp. 1448–1455, March 2018.MathSciNetGoogle Scholar
  36. [36]
    Z. Zheng, Y. Huang, L. Xie, and B. Zhu, “Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output,” IEEE Trans. on Control Systems Technology, vol. 26, no. 5, pp. 1851–1859, September 2018.CrossRefGoogle Scholar
  37. [37]
    X. Fang, F. Liu, Z. Wang, and N. Dong, “Novel disturbance-observer-based control for systems with highorder mismatched disturbances,” International Journal of Systems Science, vol. 49, no. 2, pp. 371–382, November 2017.CrossRefzbMATHGoogle Scholar
  38. [38]
    J. Huang and Z. Zhang, “Nonlinear feedback design for fixed-time tracking of a class of nonlinear systems,” International Journal of Computer Mathematics, vol. 94, no. 7, pp. 1349–1362, June 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    Y. Hong, Z. P. Jiang, and G. Feng, “Finite-time input-tostate stability and applications to finite-time control,” Proc. of the 17th IFAC World Congress, vol. 41, no. 2, pp. 2466–2471, 2008.Google Scholar
  40. [40]
    M. Basin, C. B. Panathula, and Y. Shtessel, “Multivariable continuous fixed-time second-order sliding mode control: design and convergence time estimation,” IET Control Theory and Applications, vol. 11, no. 8, pp. 1104–1111, September 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    R. Skjetne, O. Smogeli, and T. I. Fossen, “Modeling, identification, and adaptive maneuvering of CyberShip II: a complete design with experiments,” Proc. of IFAC Conference on Computer Applications in Marine Systems, vol. 37, no. 10, pp. 203–208, 2004.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.College of AutomationHarbin Engineering UniversityHeilongjiang ProvinceChina

Personalised recommendations