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Computational Methods in Applied Mathematics
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Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control

Automatic computation of conservation laws in the calculus of variations and optimal control
Authors: Gouveia, Paulo D.F.; Torres, Delfim F.M.;

Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control

Abstract

AbstractWe present analytical computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and corresponding conservation laws in optimal control theory, thus making useful in practice the theoretical results recently obtained in the literature. A Maple implementation is provided and several illustrative examples are given.

Keywords

FOS: Physical sciences, symmetries, Symbolic computation and algebraic computation, Optimality conditions for problems involving ordinary differential equations, Noether theorem, optimal control, FOS: Mathematics, Noether’s theorem, computer algebra, Mathematics - Optimization and Control, Mathematical Physics, Conservation laws, calculus of variations, Mathematical Physics (math-ph), Noether's theorem, Optimal control, Optimization and Control (math.OC), Computer algebra, Software, source code, etc. for problems pertaining to calculus of variations and optimal control, Variational principles of physics, conservation laws, 49K15, 49-04, 49S05, Calculus of variations, Symmetries

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
12
Average
Top 10%
Average
Green
hybrid