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Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties

  • Fengzhong Li
  • Yungang LiuEmail author
Research Paper
  • 20 Downloads

Abstract

This paper considers the global practical tracking for a class of uncertain nonlinear systems. Remarkably, the systems under investigation admit rather inherent nonlinearities, and especially allow arguably the most severe uncertainties: unknown control directions and non-parametric uncertainties. Despite this, a refined tracking objective, rather than a reduced one, is sought. That is, not only pre-specified arbitrary tracking accuracy is guaranteed, but also certain prescribed transient performance (e.g., arrival time and maximum overshoot) is ensured to better meet real applications. To solve the problem, a new tracking scheme is established, crucially introducing delicate time-varying gains to counteract the severe uncertainties and guarantee the prescribed performance. It is shown that the designed controller renders the tracking error to forever evolve within a prescribed performance funnel, through which the desired tracking objective is accomplished for the systems. Particularly, by subtly specifying the funnel, global fixed-time practical tracking (i.e., that with prescribed arrival time) and semiglobal practical tracking with prescribed maximal overshoot can be achieved for the systems. Moreover, the tracking scheme remains valid in the presence of rather less-restrictive unmodeled dynamics.

Keywords

nonlinear systems practical tracking prescribed transient performance unknown control directions non-parametric uncertainties unmodeled dynamics 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61325016, 61703237, 61873146), Natural Science Foundation of Shandong Province (Grant No. ZR2017BF034), and China Postdoctoral Science Foundation Funded Project (Grant Nos. 2017M610424, 2018T110690).

References

  1. 1.
    Ye X D, Ding Z T. Robust tracking control of uncertain nonlinear systems with unknown control directions. Syst Control Lett, 2001, 42: 1–10MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Qian C J, Lin W. Practical output tracking of nonlinear systems with uncontrollable unstable linearization. IEEE Trans Autom Control, 2002, 47: 21–36MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Trans Autom Control, 2003, 48: 1737–1749MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ilchmann A, Ryan E P, Townsend P. Tracking control with prescribed transient behaviour for systems of known relative degree. Syst Control Lett, 2006, 55: 396–406MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Labiod S, Guerra T M. Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems. Fuzzy Sets Syst, 2007, 158: 1126–1137MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gong Q, Qian C J. Global practical tracking of a class of nonlinear systems by output feedback. Automatica, 2007, 43: 184–189MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sun Z Y, Liu Y G. Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Autom Sin, 2008, 34: 984–989MathSciNetCrossRefGoogle Scholar
  8. 8.
    Yan X H, Liu Y G. Global practical tracking for high-order uncertain nonlinear systems with unknown control directions. SIAM J Control Optim, 2010, 48: 4453–4473MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    BenAbdallah A, Khalifa T, Mabrouk M. Adaptive practical output tracking control for a class of uncertain nonlinear systems. Int J Syst Sci, 2014, 46: 1421–1431MathSciNetzbMATHGoogle Scholar
  10. 10.
    Bechlioulis C P, Rovithakis G A. A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems. Automatica, 2014, 50: 1217–1226MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Miller D E, Davison E J. An adaptive controller which provides an arbitrarily good transient and steady-state response. IEEE Trans Autom Control, 1991, 36: 68–81MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Chowdhury D, Khalil H K. Funnel control of higher relative degree systems. In: Proceedings of American Control Conference, Seattle, 2017. 598–603Google Scholar
  13. 13.
    Tang Z L, Ge S S, Tee K P, et al. Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints. IEEE Trans Syst Man Cybern Syst, 2016, 46: 1618–1629CrossRefGoogle Scholar
  14. 14.
    Liu Y J, Tong S, Chen C L P, et al. Adaptive NN control using integral barrier lyapunov functionals for uncertain nonlinear block-triangular constraint systems. IEEE Trans Cybern, 2017, 47: 3747–3757CrossRefGoogle Scholar
  15. 15.
    Xue L R, Zhang W H, Xie X J. Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics. Sci China Inf Sci, 2017, 60: 122201MathSciNetCrossRefGoogle Scholar
  16. 16.
    Rui C, Reyhanoglu M, Kolmanovsky I, et al. Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. In: Proceedings of the 36th Conference on Decision and Control, San Diego, 1997. 3998–4003CrossRefGoogle Scholar
  17. 17.
    Su Z G, Qian C J, Shen J. Interval homogeneity-based control for a class of nonlinear systems with unknown power drifts. IEEE Trans Autom Control, 2017, 62: 1445–1450MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Sun Z Y, Yun M M, Li T. A new approach to fast global finite-time stabilization of high-order nonlinear system. Automatica, 2017, 81: 455–463MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Coron J M, Praly L. Adding an integrator for the stabilization problem. Syst Control Lett, 1991, 17: 89–104MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lin W, Qian C J. Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Syst Control Lett, 2000, 39: 339–351MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Yan X H, Liu Y G. The further result on global practical tracking for high-order uncertain nonlinear systems. J Syst Sci Complex, 2012, 25: 227–237MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Berger T, Le H H, Reis T. Funnel control for nonlinear systems with known strict relative degree. Automatica, 2018, 87: 345–357MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Li F Z, Liu Y G. Prescribed-performance control design for pure-feedback nonlinear systems with most severe uncertainties. SIAM J Control Optim, 2018, 56: 517–537MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Li F Z, Liu Y G. Control design with prescribed performance for nonlinear systems with unknown control directions and nonparametric uncertainties. IEEE Trans Autom Control, 2018, 63: 3573–3580MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Hackl C M, Hopfe N, Ilchmann A, et al. Funnel control for systems with relative degree two. SIAM J Control Optim, 2013, 51: 965–995MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Hartman P. Ordinary Differential Equations. 2nd ed. Philadelphia: SIAM, 2002CrossRefzbMATHGoogle Scholar
  27. 27.
    Yan X H, Liu Y G, Wang Q G. Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients. J Syst Sci Complex, 2015, 28: 30–46MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Ilchmann A, Ryan E P. Asymptotic tracking with prescribed transient behaviour for linear systems. Int J Control, 2006, 79: 910–917MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Control Science and EngineeringShandong UniversityJinanChina

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