Single-parameter Stochastic Extremum Seeking

Part of the Communications and Control Engineering book series (CCE)

Abstract

The first extremum seeking algorithm is introduced for single-input problems. The stability of the algorithm is studied rigorously using averaging theorems developed in earlier chapters. The reader is eased into the analysis techniques by first considering static quadratic maps for the systems being optimized, and then generalizing to systems with non-quadratic equilibrium maps and dynamics.

Keywords

Average System Stochastic Perturbation Perturbation Signal Average Theorem Sinusoidal Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 6.
    Ariyur KB, Krstic M (2003) Real-time optimization by extremum seeking control. Wiley, Hoboken MATHCrossRefGoogle Scholar
  2. 69.
    Krieger JP, Krstic M (2011) Extremum seeking based on atmospheric turbulence for aircraft endurance. AIAA J Guid Control Dyn 34:1876–1885 CrossRefGoogle Scholar
  3. 71.
    Krstic M, Wang HH (2000) Stability of extremum seeking feedback for general nonlinear dynamic systems. Automatica 36:595–601 MathSciNetMATHCrossRefGoogle Scholar
  4. 79.
    Kushner HJ, Yin G (2003) Stochastic approximation and recursive algorithms and applications, 2nd edn. Springer, Berlin MATHGoogle Scholar
  5. 89.
    Liu S-J, Krstic M (2010) Stochastic averaging in continuous time and its applications to extremum seeking. IEEE Trans Autom Control 55(10):2235–2250 MathSciNetCrossRefGoogle Scholar
  6. 98.
    Manzie C, Krstic M (2009) Extremum seeking with stochastic perturbations. IEEE Trans Autom Control 54:580–585 MathSciNetCrossRefGoogle Scholar
  7. 132.
    Spall JC (2003) Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley-Interscience, New York MATHCrossRefGoogle Scholar
  8. 137.
    Tan Y, Nešić D, Mareels IMY (2006) On non-local stability properties of extremum seeking controllers. Automatica 42:889–903 MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Department Mechanical & Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

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