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Journal of Vibration and Control
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Isoperimetric Problems on Time Scales with Nabla Derivatives

Ricardo Almeida

Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Delfim F.M. Torres

Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal, delfim{at}ua.pt

We prove a necessary optimality condition for isoperimetric problems under nabla-differentiable curves. As a consequence, the recent results of Caputo (2008), 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 the application of our main result to a dynamic optimization problem from economics.

Key Words: Control • isoperimetric problems • nabla derivatives • time scales.

This version was published on June 1, 2009

Journal of Vibration and Control, Vol. 15, No. 6, 951-958 (2009)
DOI: 10.1177/1077546309103268
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