NDLI: On the regularity of optimal controls for state constrained problems

Content Provider	IEEE Xplore Digital Library
Author	Shvartsman, I.A. Vinter, R.B.
Copyright Year	2004
Description	Author affiliation: Imperial Coll., London, UK (Shvartsman, I.A.; Vinter, R.B.)
Abstract	In this paper we summarize new results on the regularity of optimal controls for dynamic optimization problems with functional inequality constraints, a control constraint expressed in terms of a general closed convex set and a coercive cost function. Recently it has been shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters, provided the control constraint set is non-time varying. We show that, if the control constraint set, regarded as a time dependent multifunction, is merely Lipschitz continuous with respect to the time variable, then optimal controls can fail to be Lipschitz continuous. In these circumstance, however, a weaker regularity property (Holder continuity with Holder index 1/2) can be established. On the other hand, Lipschitz continuity of optimal controls is guaranteed for time varying control sets under a positive linear independence hypothesis, when the control constraint sets are described, at each time, by a finite collection of functional inequalities.
Starting Page	2285
Ending Page	2290
File Size	146191
Page Count	6
File Format	PDF
ISBN	0780386825
ISSN	01912216
DOI	10.1109/CDC.2004.1428729
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-12-14
Publisher Place	Bahamas
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Cost function Constraint optimization Educational institutions Convergence of numerical methods Qualifications
Content Type	Text
Resource Type	Article

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