Isoperimetric problems on time scales with nabla derivatives
Optimization and Control
2009-05-21 v1
Abstract
We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of [M.R. Caputo, A unified view of ostensibly disparate isoperimetric variational problems, Appl. Math. Lett. (2008), doi:10.1016/j.aml.2008.04.004], that put together seemingly dissimilar optimal control problems in economics and physics, are extended to a generic time scale. We end with an illustrative example of application of our main result to a dynamic optimization problem from economics.
Cite
@article{arxiv.0811.3650,
title = {Isoperimetric problems on time scales with nabla derivatives},
author = {Ricardo Almeida and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0811.3650},
year = {2009}
}
Comments
This is a preprint of an article whose final and definitive form will be published in the Journal of Vibration and Control. Date Accepted: November 21, 2008