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On Stochastic Extremum Seeking via Adaptive Perturbation–Demodulation Loop

Author

Listed:
  • Miloje S. Radenković

    (University of Colorado Denver)

  • Miloš S. Stanković

    (University of Belgrade
    Singidunum University
    Vlatacom Institute)

  • Srdjan S. Stanković

    (Vlatacom Institute
    University of Belgrade)

Abstract

In this paper, we propose a stochastic approximation algorithm for optimization of functions based on an adaptive extremum seeking method. The essence of this method is to approximate the gradient direction by introduction of a probing sequence, that is added to approximations and subsequently demodulated using an adaptive gain. Assuming that the probing and the demodulation signals are martingale difference sequences with adaptive diminishing gains, it is proved that the approximations converge almost surely to the optimizing value, under mild constraints on the measurement disturbance, and without assuming a priori boundedness of the approximation sequence. The measurement disturbance can contain a stochastic component, as well as a mean-square bounded deterministic component. The stochastic component can be nonstationary colored noise or a state-dependent random sequence.

Suggested Citation

  • Miloje S. Radenković & Miloš S. Stanković & Srdjan S. Stanković, 2018. "On Stochastic Extremum Seeking via Adaptive Perturbation–Demodulation Loop," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1008-1024, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1380-8
    DOI: 10.1007/s10957-018-1380-8
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    References listed on IDEAS

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    1. Takayuki Wada & Yasumasa Fujisaki, 2016. "Stopping Rules for Optimization Algorithms Based on Stochastic Approximation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 568-586, May.
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