Isoperimetric problems on time scales with nabla derivatives

Details Isoperimetric problems on time scales with nabla derivatives Isoperimetric problems on time scales with nabla derivatives

2008-11-21

arxiv.org/abs/0811.3650v1

Journal of Vibration and Control, Vol. 15 (2009), no. 6, 951-958

Mathematics

Optimization and Control

This is a preprint of an article whose final and definitive form will be published in the Journal of Vibration and Control. Da

Scientific paper

10.1177/1077546309103268

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.

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