Noether's symmetry Theoremfor variational and optimal control problems with time delay

Gastão S. F.  Frederico; Delfim F. M. Torres

doi:10.3934/naco.2012.2.619

Article Contents

2012, Volume 2, Issue 3: 619-630. Doi: 10.3934/naco.2012.2.619

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Noether's symmetry Theorem for variational and optimal control problems with time delay

Gastão S. F. Frederico^1, and
Delfim F. M. Torres^2,

1.
Department of Science and Technology, University of Cape Verde, Praia, Santiago, Cape Verde, Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro
2.
CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro

Received: February 29, 2012

Revised: February 29, 2012

Published: July 2012

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Abstract

We extend the DuBois--Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.

Keywords:

Time delay,
invariance,
symmetries,
constants of motion,
DuBois--Reymond necessary optimality condition,
Noether's theorem.

Mathematics Subject Classification: Primary: 49K05, 49S05.

Citation:

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References

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