Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Caratheodory-Equivalence, Noether Theorems, and Tonelli Full-Regularity
  in the Calculus of Variations and Optimal Control   We study, in a unified way, the following questions related to the properties
of Pontryagin extremals for optimal control problems with unrestricted
controls: i) How the transformations, which define the equivalence of two
problems, transform the extremals? ii) How to obtain quantities which are
conserved along any extremal? iii) How to assure that the set of extremals
include the minimizers predicted by the existence theory? These questions are
connected to: i) the Caratheodory method which establishes a correspondence
between the minimizing curves of equivalent problems; ii) the interplay between
the concept of invariance and the theory of optimality conditions in optimal
control, which are the concern of the theorems of Noether; iii) regularity
conditions for the minimizers and the work pioneered by Tonelli.

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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio