Related papers: Noether's theorem for higher-order variational pro…
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymond necessary optimality conditions as well as a higher-order…
We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing…
We obtain a generalized Euler-Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.
We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful…
We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollaries, the DuBois-Reymond necessary optimality condition and the…
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…
We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether's theorem without transformation of the…
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…
We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
We obtain a nonsmooth higher-order extension of Noether's symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed…
The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal's necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using…
We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and…
The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought,…
We begin by presenting the classical deterministic problems of the calculus of variations, with emphasis on the necessary optimality conditions of Euler-Lagrange and the Noether theorem. As examples of application, we obtain the…
We prove a generalization of Noether's theorem for optimal control problems defined on time scales. Particularly, our results can be used for discrete-time, quantum, and continuous-time optimal control problems. The generalization involves…
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…
We extend the second Noether theorem to optimal control problems which are invariant under symmetries depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. As far as we consider a…
We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary optimality condition for nabla problems of the calculus of variations on time scales.