Optimal control solutions to the maximum volume isoperimetric pillars problem

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper extends the isoperimetric problem. The problem is to find an enclosed cross-sectional/base region of a pillar defined by a simple closed curve of fixed perimeter such that the volume of the constructed pillar, bounded above by a relatively smooth ceiling, is maximized. Green's Theorem is applied in the formulation of the problem such that the problem can be transformed into canonical form handled by MISER3. For the case of multiple pillars, a novel elliptic separation technique is developed for multiple pillars constructions. This technique is used to ensure that the cross-sectional regions of any pillars are separated. Illustrative examples are provided to demonstrate the effectiveness of the technique developed.
Original languageEnglish
Pages (from-to)1201-1208
Number of pages8
JournalAutomatica
Volume44
Issue number5
DOIs
Publication statusPublished - 1 May 2008

Keywords

  • Elliptic separation technique
  • Green's theorem
  • Isoperimetric problem
  • Optimal control
  • Pontryagin's maximum principle

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this