An Optimal Control Formulation of the Blaschke-Lebesgue Theorem

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.

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Document Details

Document Type
Technical Report
Publication Date
Aug 22, 1988
Accession Number
ADA200939

Entities

People

  • Mostafa Ghandehari

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bodies
  • Calculus
  • Calculus Of Variations
  • Classification
  • Computer Science
  • Control Theory
  • Convex Bodies
  • Convex Sets
  • Curvature
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Industrial Engineering
  • Mathematics
  • New York
  • Schools
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.