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Quadratures of Pontryagin Extremals for Optimal Control Problems
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TLDR
In this article, the integrability of optimal control problems with control taking values on open sets is investigated and a sufficient condition for the integrinability by quadratures is obtained.Abstract:
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.read more
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Constants of Motion for Non-Differentiable Quantum Variational Problems ∗
TL;DR: In this paper, the authors extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting, and obtain constants of motion for some linear and nonlinear variants of the Schrodinger equation.
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Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
TL;DR: In this article, the authors extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting, covering problems of the calculus of variations and optimal control with delays.
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Symbolic Computation of Variational Symmetries in Optimal Control
TL;DR: In this paper, a computer algebra system was used to compute optimal control variational symmetries up to a gauge term, which were then used to obtain families of Noether's first integrals, possibly in the presence of nonconservative external forces.
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Conservation laws for invariant functionals containing compositions
TL;DR: In this article, a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions is presented, with the help of the new obtained condition, a Noether-type theorem is proved.
Journal ArticleDOI
Conservation laws for invariant functionals containing compositions
TL;DR: In this article, a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions is presented, with the help of the new obtained condition, a Noether-type theorem is proved.
References
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Book
Mathematical Theory of Optimal Processes
TL;DR: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems as discussed by the authors, which can be applied in a variety of situations, including linear equations with variable coefficients.
Journal ArticleDOI
The Mathematical Theory of Optimal Processes
Richard Bellman,L. S. Pontryagin,V. G. Boltyanskii,Revaz Valerianovich Gamkrelidze,E. F. Mishchenko,K. N. Trirogoff,Lucien W. Neustadt +6 more
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Mathematical aspects of classical and celestial mechanics
TL;DR: The main purpose of the book as discussed by the authors is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications.
Journal ArticleDOI
The Mathematical Theory of Optimal Processes.
Journal ArticleDOI
Invariant Variation Problems
TL;DR: In this paper, a combination of the methods of the formal calculus of variations with those of Lie's group theory is presented, which is not new; Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker, Weyl and Klein)1 for special infinite groups.