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Stochastic exit time problems arising in process control

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Title: Stochastic exit time problems arising in process control
Authors: Clark, JMC
Vinter, RB
Item Type: Journal Article
Abstract: This paper concerns the problem of controlling a stochastic system, with small noise parameter, to prevent it leaving a safe region of the state space. Such problems arise in flow control and other areas. We consider a formulation of the problem, in which a control is sought, to maximize a cost which is related to the expected exit time, but modified to reduce the probability of an early exit, according to a specified level of risk aversion (‘risk sensitive’ stochastic control). Formally letting the noise parameter tend to zero, we find that the optimal control strategy for this problem coincides with the optimal feedback control strategy for a differential game. We identify a class of differential games arising in this way, the so called decomposable differential games, for which the optimal control strategy can be easily obtained and illustrate the proposed solution technique by applying it to a flow control problem arising in process systems engineering.
Issue Date: 15-Mar-2012
Date of Acceptance: 18-Dec-2011
URI: http://hdl.handle.net/10044/1/40484
DOI: http://dx.doi.org/10.1080/17442508.2011.652117
ISSN: 1744-2516
Publisher: Taylor and Francis
Start Page: 667
End Page: 681
Journal / Book Title: Stochastics-An International Journal of Probability and Stochastic Processes
Volume: 84
Issue: 5-6
Copyright Statement: © 2012 Taylor & Francis. This is an Author's Accepted Manuscript of an article published in Stochastics, available online at: http://dx.doi.org/10.1080/17442508.2011.652117.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/G066477/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Statistics & Probability
stochastic control
exit problems
risk-sensitive control
differential games
01 Mathematical Sciences
15 Commerce, Management, Tourism And Services
Publication Status: Published
Appears in Collections:Electrical and Electronic Engineering
Faculty of Engineering