NDLI: Stochastic optimal control subject to variational norm uncertainty: viscosity subsolution for generalized HJB inequality

Content Provider	IEEE Xplore Digital Library
Author	Rezaei, F. Charalambous, C.D. Ahmed, N.U.
Copyright Year	2009
Description	Author affiliation: Department of Electrical Engineering, University of Cyprus, Nicosia, Cyprus (Charalambous, C.D.) \|\| School of Information Technology and Engineering, University of Ottawa, 800 King Edward Ave., Canada (Rezaei, F.; Ahmed, N.U.)
Abstract	This paper is concerned with optimization of stochastic uncertain systems, when systems are described by measures and the pay-off by a linear functional on the space of measure, on general abstract spaces. Robustness is formulated as a minimax game, in which the control seeks to minimize the pay-off over the admissible controls while the measure aims at maximizing the pay-off over the total variational distance uncertainty constraint between the uncertain and nominal measures. This paper is a continuation of the abstract results in [1], where existence of the maximizing measure over the total variational distance constraint is established, while the maximizing payoff is shown to be equivalent to an optimization of a payoff which is a linear combination of L1 and L∞ norms. The maximizing measure is constructed from a convex combination of a sequence of tilted measures and the nominal measure. Here emphasis is geared towards the application of the abstract results to uncertain continuous-time controlled stochastic differential equations, in which the control seeks to minimize the pay-off while the measure seeks to maximize it over the total variational distance constraint. The maximization over the total variational distance constraint is resolved resulting in an equivalent pay-off which is a non-linear functional of the nominal measure of non-standard form. The minimization over the admissible controls of the non-linear functional is addressed by deriving a HJB inequality and viscosity subsolution. Throughout the paper the formulation and conclusions are related to previous work found in the literature.
Starting Page	1587
Ending Page	1592
File Size	402379
Page Count	6
File Format	PDF
ISBN	9781424438716
ISSN	01912216
DOI	10.1109/CDC.2009.5400155
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-15
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Optimal control Viscosity Stochastic systems Uncertain systems Extraterrestrial measurements Robust control Minimax techniques Measurement uncertainty Constraint optimization
Content Type	Text
Resource Type	Article

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