Lipschitz selections of convexifications of pseudo-lipschitz multifunctions and the Lipschitz maximum principle for differential inclusions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We prove that, if X, Y are finite-dimensional real linear spaces and F : X → 2Y is a multifunction that has the pseudo-Lipschitz property at a point (x0, y0) 2 Graph(F), then for every ε > 0 there exists a Lipschitz multifunction Vε : N(ε) → 2Y, defined on a neighborhood N(ε) of x0, such that (i) Vε has compact convex values, (ii) Vε(x 0) = {y0}, and (iii) for every x ∈ N(ε), V ε(x) is a subset of the convex hull co(Fε(x)) of the intersection Fε(x) of F(x) with the closed ε-ball centered at y0. In particular, this implies the existence of a Lipschitz single-valued selection fε of co(Fε) near x 0 satisfying fε(x0) = y0.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3403-3408
Number of pages6
ISBN (Print)9781424477456
DOIs
StatePublished - 2010
Event49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States
CityAtlanta
Period12/15/1012/17/10

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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