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A generalized fractional calculus of variations

Odzijewicz T., Malinowska A. B., Torres D. F. M.

Control and Cybernetics

2013

Vol. 42, no. 2

443--458

We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, transversality conditions for free boundary value problems, and a generalized Noether type theorem.

Symbolic computation of variational symmetries in optimal control

Gouveia P. D., Torres D. F., Rocha E. A.

Control and Cybernetics

2006

Vol. 35, no 4

831-849

We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for a sub-Riemannian nilpotent problem (2,3,5,8).

Quadratures of Pontryagin extremals for optimal control problems

Rocha E. A., Torres D. F.

Control and Cybernetics

2006

Vol. 35, no 4

948-963

We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values on open sets is obtained. We illustrate our approach on some problems taken from the literature. An alternative proof of the integrability of the sub-Riemannian nilpotent Lie group of type (2,3,5) is also given.

Conservation laws for coupled magnetothermoelasticity

Bytner S.

Journal of Technical Physics

1998

Vol. 39, no 2

349-355

Noether's theorem on variational principles invariant under a group of infinitesimal transformations is used to establish two conservation laws associated with isotropic linear magnetothermoelasticity.