𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An Optimal Control Formulation of the Blaschke–Lebesgue Theorem

✍ Scribed by Mostafa Ghandehari

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
118 KB
Volume
200
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

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. ᮊ

📜 SIMILAR VOLUMES

An Unconstrained Calculus of Variations
An Unconstrained Calculus of Variations Formulation for Generalized Optimal Control Problems and for the Constrained Problem of Bolza
✍ J. Gregory; C.T. Lin 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 513 KB

This paper has two main ideas. The first idea is that constrained problems in optimal control theory and the calculus of variations can be associated with unconstrained calculus of variations problems by using multipliers. This allows us to obtain a true Lagrange multiplier rule where both the origi