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Global practical tracking by output-feedback for nonlinear systems with unknown growth rate

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Abstract

This paper is devoted to the global practical tracking by output-feedback for a class of uncertain nonlinear systems with only the tracking error measurable. Different from the closely related works, the systems have unmeasured states dependent growth with unknown constant rate, and the reference signal, as well as its first order derivative, has unknown bound. Mainly because of these, the tracking problem can hardly be solved by straightforwardly extending the existing results. In the paper, motivated by the related stabilization results, and flexibly using the ideas of universal control and dead zone, an adaptive output-feedback controller is designed to make the tracking error prescribed arbitrarily small after a finite time while keeping all the states of the closed-loop system bounded. A numerical example demonstrates the effectiveness of the theoretical results.

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References

  1. Pan Z G, Başar T. Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems. IEEE Trans Automat Contr, 1998, 43: 1066–1083

    Article  MATH  Google Scholar 

  2. Jiang Z P. Decentralized and adaptive nonlinear tracking large-scale systems via output feedback. IEEE Trans Automat Contr, 2000, 45: 2122–2128

    Article  MATH  Google Scholar 

  3. Krishnamurthy P, Khorrami F, Jiang Z P. Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form. IEEE Trans Automat Contr, 2002, 47: 814–819

    Article  MathSciNet  Google Scholar 

  4. Ryan E P. A nonlinear universal servomechanism. IEEE Trans Automat Contr, 1994, 39: 753–761

    Article  MATH  Google Scholar 

  5. Ilchmann A, Ryan E P. Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise. Automatica, 1994, 30: 337–346

    Article  MathSciNet  MATH  Google Scholar 

  6. Ye X D, Ding Z T. Robust tracking control of uncertain nonlinear systems with unknown control directions. Syst Contr Lett, 2001, 42: 1–10

    Article  MathSciNet  Google Scholar 

  7. Qian C J, Lin W. Practical output tracking of nonlinear systems with uncontrollable unstable linearization. IEEE Trans Automat Contr, 2002, 47: 21–35

    Article  MathSciNet  Google Scholar 

  8. Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Trans Automat Contr, 2003, 48: 1737–1749

    Article  MathSciNet  Google Scholar 

  9. Sun Z Y, Liu Y G. Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Automat Sin, 2008, 34: 984–989

    Article  MathSciNet  Google Scholar 

  10. Mareels I M Y. A simple selftuning controller for stably invertible systems. Syst Contr Lett, 1984, 4: 5–16

    Article  MathSciNet  MATH  Google Scholar 

  11. Ye X D. Universal λ-tracking for nonlinearly-perturbed systems without restrictions on the relative degree. Automatica, 1999, 35: 109–119

    Article  MATH  Google Scholar 

  12. Bullinger E, Allgöwer F. Adaptive λ-tracking for nonlinear higher relative degree systems. Automatica, 2005, 41: 1191–1200

    Article  MATH  Google Scholar 

  13. Gong Q, Qian C J. Global practical tracking of a class of nonlinear systems by output feedback. Automatica, 2007, 43: 184–189

    Article  MathSciNet  MATH  Google Scholar 

  14. Miller D E, Davison E J. An adaptive controller which provides an arbitrarily good transient and steady-state response. IEEE Trans Automat Contr, 1991, 36: 68–81

    Article  MathSciNet  MATH  Google Scholar 

  15. Ilchmann A, Ryan E P, Sangwin C J. Tracking with prescribed transient behaviour. ESAIM Contr Optim Calc Var, 2002, 7: 471–493

    Article  MathSciNet  MATH  Google Scholar 

  16. Ilchmann A, Ryan E P, Townsend P. Tracking with prescribed transient behavior for nonlinear systems of known relative degree. SIAM J Contr Optim, 2007, 46: 210–230

    Article  MathSciNet  MATH  Google Scholar 

  17. Qian C J, Schrader C B, Lin W. Global regulation of a class of uncertain nonlinear systems using time-varying output feedback. In: Proceedings of 2003 American Control Conference. Denver, 2003. 1542–1547

  18. Lei H, Lin W. Universal adaptive control of nonlinear systems with unknown growth rate by output feedback. Automatica, 2006, 42: 1783–1789

    Article  MathSciNet  MATH  Google Scholar 

  19. Praly L, Jiang Z P. Linear output feedback with dynamic high gain for nonlinear systems. Syst Contr Lett, 2004, 53: 107–116

    Article  MathSciNet  MATH  Google Scholar 

  20. Hale J K. Ordinary Differential Equations. 2nd ed. New York: Krieger, 1980

    MATH  Google Scholar 

  21. Min Y Y, Liu Y G. Barbălat lemma and its application in analysis of system stability (in Chinese). J Shandong Univ (Engin Sci), 2007, 37: 51–55

    Google Scholar 

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    XueHua Yan & YunGang Liu

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  1. XueHua Yan
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  2. YunGang Liu
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Correspondence to YunGang Liu.

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Yan, X., Liu, Y. Global practical tracking by output-feedback for nonlinear systems with unknown growth rate. Sci. China Inf. Sci. 54, 2079–2090 (2011). https://doi.org/10.1007/s11432-011-4253-4

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  • DOI: https://doi.org/10.1007/s11432-011-4253-4

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