Circle-Criterion Observers and Their Feedback Applications: An Overview

  • Murat Arcak
Part of the Systems and Control: Foundations & Applications book series (SCFA)

Summary

This chapter gives an overview of the “circle-criterion” design of nonlinear observers, initiated and further developed by the author in a series of papers. It summarizes these results in a concise and unified manner and illustrates them with physically motivated design examples from fuel cell power systems, ship control, and active magnetic bearing systems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aamo O, Arcak M, Fossen T, Kokotović P (2001) Global output tracking control of a class of Euler-Lagrange systems with monotonic nonlinearities in the velocities. International Journal of Control 74(7):649–658MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Arcak M (2005) Certainty-equivalence output-feedback design with circle-criterion observers. IEEE Transactions on Automatic Control 50(6):905–909MathSciNetCrossRefGoogle Scholar
  3. 3.
    Arcak M, Gorgun H, Pedersen L, Varigonda S (2004) A nonlinear observer design for fuel cell hydrogen estimation. IEEE Transactions on Control Systems Technology 12(1):101–110CrossRefGoogle Scholar
  4. 4.
    Arcak M, Kokotović P (2001a) Nonlinear observers: A circle criterion design and robustness analysis. Automatica 37(12):1923–1930MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Arcak M, Kokotović P (2001b) Observer-based control of systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control 4(7):1146–1151CrossRefGoogle Scholar
  6. 6.
    Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics. SIAM, Philadelphia, PAGoogle Scholar
  7. 7.
    Fan X, Arcak M (2003) Observer design for systems with multivariable monotone nonlinearities. Systems and Control Letters 50(4):319–330MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kazantzis N, Kravaris C (1998) Nonlinear observer design using Lyapunov’s auxiliary theorem. Systems and Control Letters 34(5):241–247MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Khalil H (1999) High-gain observers in nonlinear feedback control In: Nijmeijer H, Fossen T (eds), New directions in nonlinear observer design, 249–268. Springer-Verlag, New YorkGoogle Scholar
  10. 10.
    Khalil H (2002) Nonlinear systems. Prentice-Hall, Upper Saddle River, NJMATHGoogle Scholar
  11. 11.
    Kokotović P (1992) The joy of feedback: nonlinear and adaptive. IEEE Control Systems Magazine 12:7–17CrossRefGoogle Scholar
  12. 12.
    Krener A, Isidori A (1983) Linearization by output injection and nonlinear observers. Systems and Control Letters 3:47–52MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Lohmiller W, Slotine JJ (1998) On contraction analysis for nonlinear systems. Automatica 34:683–696MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Praly L, Arcak M (2004) A relaxed condition for stability of nonlinear observer-based controllers. Systems and Control Letters53(3–4):311–320MathSciNetCrossRefGoogle Scholar
  15. 15.
    Raghavan S, Hedrick J (1994) Observer design for a class of nonlinear systems. International Journal of Control 59:515–528MATHMathSciNetGoogle Scholar
  16. 16.
    Thau F (1973) Observing the state of non-linear dynamic systems. International Journal of Control 17:471–479MATHGoogle Scholar
  17. 17.
    Tsiotras P, Arcak M (2005) Low-bias control of AMB subject to voltage saturation: State-feedback and observer designs. IEEE Transactions on Control Systems Technology 13(2):262–273CrossRefGoogle Scholar
  18. 18.
    Zames G (1966) On the input-output stability of time-varying nonlinear feedback systems-Parts I and II. IEEE Transactions on Automatic Control 11:228–238, 465–476CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Murat Arcak
    • 1
  1. 1.Electrical, Computer, and Systems Engineering DepartmentRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations