Noether’s Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
نویسندگان
چکیده
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.
منابع مشابه
Constants of Motion for Non-Differentiable Quantum Variational Problems
We extend the DuBois-Reymond necessary optimality condition and Noether’s symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether’s theorem are proved, covering problems of the calculus of variations with functionals defined on sets of non-differentiable functions, as well as more general non-differentiable problems of optimal control. As an ...
متن کاملNon-conservative Noether’s theorem for fractional action-like variational problems with intrinsic and observer times
We extend Noether’s symmetry theorem to fractional action-like variational problems with higher-order derivatives.
متن کاملA Proper Extension of Noether’s Symmetry Theorem for Nonsmooth Extremals of the Calculus of Variations
For nonsmooth Euler-Lagrange extremals, Noether’s conservation laws cease to be valid. We show that Emmy Noether’s theorem of the calculus of variations is still valid in the wider class of Lipschitz functions, as long as one restrict the Euler-Lagrange extremals to those which satisfy the DuBois-Reymond necessary condition. In the smooth case all EulerLagrange extremals are DuBois-Reymond extr...
متن کاملA New Optimal Solution Concept for Fuzzy Optimal Control Problems
In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...
متن کاملCape Verde Praia , Santiago , Cape Verde
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 optimal control are given.
متن کامل