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On the Noether theorem for optimal control
 European Journal of Control
"... 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 conserved quantities previously obtained in the literature f ..."
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Cited by 38 (31 self)
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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 conserved quantities previously obtained in the literature for nonconservative problems of mechanics and the calculus of variations are derived.
Symbolic computation of variational symmetries in optimal control, Control & Cybernetics
"... 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 i ..."
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Cited by 9 (6 self)
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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 the subRiemannian nilpotent problem (2, 3,5, 8).
Absolute extrema of invariant optimal control problems
 Commun. Appl. Anal
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Noether’s symmetry theorem for variational and optimal control problems with time delay
 Numer. Algebra Control Optim
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Abstract
, 2006
"... We extend Noether’s symmetry theorem to the fractional RiemannLiouville integral functionals of the calculus of variations recently introduced by ElNabulsi. AMS Subject Classification: 49K05, 49S05, 70H33. ..."
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We extend Noether’s symmetry theorem to the fractional RiemannLiouville integral functionals of the calculus of variations recently introduced by ElNabulsi. AMS Subject Classification: 49K05, 49S05, 70H33.
Abstract
, 2003
"... We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented. ..."
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We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
Constants of Motion for NonDifferentiable Quantum Variational Problems ∗
, 805
"... We extend the DuBoisReymond 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 nondiffere ..."
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We extend the DuBoisReymond 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 nondifferentiable functions, as well as more general nondifferentiable problems of optimal control. As an application we obtain constants of motion for some linear and nonlinear variants of the Schrödinger equation.
The original publication is available at www.springerlink.com Nonlinear Dynamics, DOI: 10.1007/s110710079309z
, 711
"... Fractional conservation laws in optimal control theory ..."
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