# American Institute of Mathematical Sciences

2012, 2(3): 619-630. doi: 10.3934/naco.2012.2.619

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

 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, Portugal 2 CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Received  March 2012 Revised  March 2012 Published  August 2012

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.
Citation: Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 619-630. doi: 10.3934/naco.2012.2.619
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