Stochastic averaging and stochastic extremum seeking
type: Item
instance of: scholarly article
title: Stochastic averaging and stochastic extremum seeking
zbMATH Open document ID: 1253.93003
DOI: 10.1007/978-1-4471-4087-0
author: Shu-Jun Liu
author: Miroslav Krstic
published in: Communications and Control Engineering
publication date: 2012-06-21T00:00:00Z
review text: This book deals with two topics: (i) stochastic averaging, which refers to approximating the evolution of an ordinary or stochastic differential equation with a noise input on a `fast' timescale by a simpler system wherein the effect of the 'fast' timescale dynamics is averaged out, and, (ii) stochastic extremum seeking, which refers to designing systems with rapidly varying noise so that their averaged system achieves a desired goal, typically a solution to a control problem. Stochastic averaging is considered in chapters 1, 3 and 4, for finite time horizon, for tracking the asymptotic behavior of systems with strong stability properties, and finally for situations under weaker hypotheses, respectively. The remainder of the book develops single- and multi-parameter stochastic extremum seeking techniques and discusses various specific classes of applications. These are: stochastic source seeking by tuning angular or forward velocity, stochastic gradient seeking and its Newton-based counterpart, and Nash equilibrium seeking in games, with special focus on quadratic games and their application to oligopoly markets and multi-agent deployment in the plane. The theoretical analysis is supported by simulations. Much of the book is based on the authors' own research.
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 70K65
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 6048955
zbMATH Keywords: stochastic averaging
zbMATH Keywords: stochastic extremum seeking
zbMATH Keywords: stochastic source seeking
zbMATH Keywords: stochastic gradient seeking
zbMATH Keywords: Nash equilibrium seeking
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4471-4087-0
OpenAlex ID: W604319556
description: scientific article; zbMATH DE number 6048955