Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac structures and reduction of optimal control problems with
  symmetries   We discuss the use of Dirac structures to obtain a better understanding of
the geometry of a class of optimal control problems and their reduction by
symmetries. In particular we will show how to extend the reduction of Dirac
structures recently proposed by Yoshimura and Marsden [Yo09] to describe the
reduction of a class of optimal control problems with a Lie group of symmetry.
We will prove that, as in the case of reduction of implicit Hamiltonian or
Lagrangian systems, the reduction of the variational principle and the
reduction of the Dirac structure describing the Pontryagin Maximum Principle
first order differential conditions coincide. Moreover they will also reproduce
E. Mart\'inez Lie algebroids reduction approach [Mr04] to optimal control
systems with symmetry. The geodesic subriemannian problem considered as an
optimal control problem on the Heisenberg group, will be discussed as a simple
example illustrating these results.

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The categories of this paper are: stat
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg