Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20000
Title: Optimal control solutions to the maximum volume isoperimetric pillars problem
Authors: Lee, YCE
Lee, HWJ 
Issue Date: 2008
Source: Automatica, 2008, v. 44, no. 5, p. 1201-1208
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.
Keywords: Elliptic separation technique
Green's theorem
Isoperimetric problem
Optimal control
Pontryagin's maximum principle
Publisher: Pergamon Press
Journal: Automatica 
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2007.09.026
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