TY - JOUR
T1 - Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation
AU - Solis, Cesar U.
AU - Clempner, Julio B.
AU - Poznyak, Alexander S.
N1 - Publisher Copyright:
© 2018 John Wiley & Sons, Ltd.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - continuous time
KW - extremum seeking
KW - integral sliding mode
KW - stochastic gradient estimation synchronous detection method
KW - stochastic optimization
UR - http://www.scopus.com/inward/record.url?scp=85056862577&partnerID=8YFLogxK
U2 - 10.1002/rnc.4408
DO - 10.1002/rnc.4408
M3 - Artículo
SN - 1049-8923
VL - 29
SP - 702
EP - 714
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
IS - 3
ER -