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Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation
Author(s) -
Solis Cesar U.,
Clempner Julio B.,
Poznyak Alexander S.
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4408
Subject(s) - control theory (sociology) , convergence (economics) , mathematical optimization , controller (irrigation) , noise (video) , integral sliding mode , gradient descent , convex function , computer science , stability (learning theory) , mode (computer interface) , gradient method , mathematics , function (biology) , regular polygon , sliding mode control , nonlinear system , control (management) , artificial intelligence , image (mathematics) , economic growth , biology , geometry , quantum mechanics , machine learning , evolutionary biology , artificial neural network , agronomy , physics , economics , operating system
Summary This paper presents a continuous‐time optimization method for an unknown convex function restricted to a dynamic plant with an available output including a stochastic noise. For solving the problem, we propose an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent approach. In order to reject from the beginning the undesirable uncertainties and perturbations of the dynamic plant, we employ the standard deterministic integral sliding mode control transforming the initial dynamic plant to the static one, and after (in fact, from the beginning of the process), we apply the gradient decedent technique. We consider time‐decreasing parameters for compensating the stochastic dynamics. We prove the stability and the mean‐square convergence of the method. To validate the exposition, we perform a numerical example simulation.