Skip to main content
SpringerLink
Log in

A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

  • Research Papers
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients. Although the existing literature has solved the problem, for n-dimensional systems, the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller; that is, the dimension of the dynamic compensator is not less than n + 1, and therefore, there exists serious overparametrization. In this paper, by defining some new unknown parameters which need dynamic updating, also by using adding a power integrator and related adaptive technique, the overparametrization is successfully solved and a new approach is given to design stabilizing adaptive controller based on only one parameter updating law. A simulation example is finally provided to demonstrate the validness of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kanellakopoulos I, Kokotović P V, Morse S. Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control, 1991, 36: 1241–1253

    Article  MATH  Google Scholar 

  2. Krstić M, Kanellakopoulos I, Kokotović P V. Nonlinear and Adaptive Control Design. New York: John Wiley & Sons, INC, 1995

    Google Scholar 

  3. Jiang Z P, Praly L. Design of robust adaptive controllers for nonlinear systems with dynamics uncertainties. Automatica, 1998, 34: 825–840

    Article  MATH  MathSciNet  Google Scholar 

  4. Ye X D, Jiang J P. Adaptive nonlinear design without a priori knowledge of control directions. IEEE Trans Autom Control, 1998, 43: 1617–1621

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhou J, Wen C Y, Zhang Y. Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Trans Autom Control, 2006, 51: 504–511

    Article  MathSciNet  Google Scholar 

  6. Pan Z, Liu Y, Shi S. Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics. Sci China Ser F-Inf Sci, 2001, 44: 292–308

    MATH  MathSciNet  Google Scholar 

  7. Liu Y, Pan Z, Shi S. Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE Trans Autom Control, 2003, 48: 509–514

    Article  MathSciNet  Google Scholar 

  8. Liu Y, Zhang J. Reduced-order observer-based control design for nonlinear stochastic systems. Syst Control Lett, 2004, 52: 123–135

    Article  MATH  Google Scholar 

  9. Liu Y, Zhang J. Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zerodynamics. SIAM J Control Opt, 2006, 45: 885–926

    Article  MATH  Google Scholar 

  10. Lin W, Qian C. Adding one power integrator: A tool for global stabilization of high order lower-triangular systems. Syst Control Lett, 2000, 39: 339–351

    Article  MATH  MathSciNet  Google Scholar 

  11. Lin W, Qian C. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans Autom Control, 2001, 46: 1061–1079

    Article  MATH  MathSciNet  Google Scholar 

  12. Lin W, Qian C. Adaptive control of nonlinear parameterized system: A nonsmooth feedback framework. IEEE Trans Autom Control, 2002, 47: 757–774

    Article  MathSciNet  Google Scholar 

  13. Lin W, Qian C. Adaptive control of nonlinearly parameterized systems: The smooth feedback case. IEEE Trans Autom Control, 2002, 47: 1249–1266

    Article  MathSciNet  Google Scholar 

  14. Lin W, Pongvuthithum R. Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback. IEEE Trans Autom Control, 2003, 48: 1809–1816

    Article  MathSciNet  Google Scholar 

  15. Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Trans Autom Control, 2003, 48: 1737–1749

    Article  MathSciNet  Google Scholar 

  16. Qian C, Lin W. Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems. IEEE Trans Autom Control, 2006, 51: 1457–1471

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Sun Z, Liu Y. Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica, 2007, 43: 1772–1783

    Article  MATH  MathSciNet  Google Scholar 

  19. Sun Z, Liu Y. Adaptive stabilization for a large class of high-order nonlinear uncertain systems. Intl J Control, 2009, 82: 1275–1287

    Article  MATH  MathSciNet  Google Scholar 

  20. Li W, Xie X. Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable. Automatica, 2009, 45: 498–503

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Jian Zhang & YunGang Liu

Authors
  1. Jian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YunGang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to YunGang Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, J., Liu, Y. A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems. Sci. China Inf. Sci. 54, 1419–1429 (2011). https://doi.org/10.1007/s11432-011-4299-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4299-3

Keywords

Search

Navigation