An optimal control formulation of the Blaschke-Lebesgue theorem
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Authors
Ghandehari, Mostafa
Subjects
Convex sets and related geometric topics
Calculus of variation and optimal control
Calculus of variation and optimal control
Advisors
Date of Issue
1988-08
Date
1988-08
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
The Blaschke-Lebesgue theorem states that of all plane sets of given constant width the Reuleaux triangle has least area. The area to be minimized is a functional involving the support function and the radius of curvature of the set. The support function satisfies a second order ordinary differential equation where the radius of curvature is the control parameter. The radius of curvature of a plane set of constant width is non-negative and bounded above. Thus we can formulate and analyze the Blaschke-Lebesgue theorem as an optimal control problem. Keywords: Calculus of variation and optimal control. (KR) Limitation Statement:
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-53-88-008
Sponsors
Naval postgraduate School
Monterey, CA
Funder
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.