On Stochastic Extremum Seeking via Adaptive Perturbation–Demodulation Loop

Miloje S. Radenković (), Miloš S. Stanković () and Srdjan S. Stanković ()
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Miloje S. Radenković: University of Colorado Denver
Miloš S. Stanković: University of Belgrade
Srdjan S. Stanković: Vlatacom Institute

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 14, 1008-1024

Abstract: 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.

Keywords: Stochastic approximations; Extremum seeking; Almost sure convergence; Perturbation–demodulation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1380-8

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