Multifunctions of bounded variation

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Title: Multifunctions of bounded variation
Authors: Vinter, RB
Item Type: Journal Article
Abstract: Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set F(t,x). Certain properties of state trajectories can be derived when it is assumed that F(t,x) is merely measurable w.r.t. the time variable t . But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the time dependence. Stronger forms of necessary conditions for minimizing state trajectories can be derived, for example, when F(t,x) is Lipschitz continuous w.r.t. time. It has recently become apparent that significant addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that F(t,x) has bounded variation w.r.t. time. This paper introduces a new concept of multifunctions F(t,x) that have bounded variation w.r.t. time near a given state trajectory, of special relevance to control. We provide an application to sensitivity analysis.
Issue Date: 18-Nov-2015
Date of Acceptance: 20-Aug-2015
URI: http://hdl.handle.net/10044/1/38874
DOI: http://dx.doi.org/10.1016/j.jde.2015.10.033
ISSN: 1090-2732
Publisher: Elsevier
Start Page: 3350
End Page: 3379
Journal / Book Title: Journal of Differential Equations
Volume: 260
Issue: 4
Copyright Statement: © 2015 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: PITN-GA-2010-264735
Keywords: Science & Technology
Physical Sciences
Mathematics
Differential inclusions
Optimal control
Bounded variation
Sensitivity
REGULARITY
General Mathematics
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status: Published
Appears in Collections:Faculty of Engineering
Electrical and Electronic Engineering



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