NDLI: Stochastic Averaging in Discrete Time and its Applications to Extremum Seeking

Content Provider	IEEE Xplore Digital Library
Author	Shu-Jun Liu Krstic, M.
Copyright Year	1963
Abstract	We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by defining two average systems (one is continuous time, the other is discrete time), we develop discrete-time stochastic averaging theorem for locally Lipschitz nonlinear systems with stochastic perturbation. Our results only need some simple and applicable conditions, which are easy to verify, and remove a significant restriction present in existing results: global Lipschitzness of the nonlinear vector field. Secondly, we provide a discrete-time stochastic extremum seeking algorithm for a static map, in which measurement noise is considered and an ergodic discrete-time stochastic process is used as the excitation signal. Finally, for discrete-time nonlinear dynamical systems, in which the output equilibrium map has an extremum, we present a discrete-time stochastic extremum seeking scheme and, with a singular perturbation reduction, we prove the stability of the reduced system. Compared with classical stochastic approximation methods, while the convergence that we prove is in a weaker sense, the conditions of the algorithm are easy to verify and no requirements (e.g., boundedness) are imposed on the algorithm itself.
Sponsorship	IEEE Control Systems Society
Starting Page	90
Ending Page	102
Page Count	13
File Size	459976
File Format	PDF
ISSN	00189286
Volume Number	61
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2016-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Stability analysis Convergence Approximation algorithms Noise measurement Noise Algorithm design and analysis stochastic perturbation Stochastic averaging extremum seeking Extremum seeking stochastic averaging
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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