Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Attainable set for rank 3 step 2 free Carnot group with positive
  controls   We find the attainable set for a control system on the free Carnot group of
rank $3$ and step $2$ with positive controls. This kind of control systems is
connected with the theory of free Lie semigroups; with some estimates for
probabilities of inequalities for independent random variables; with the
nilpotent approximation of robotic control systems and with contour recovering
without cusps in image processing. We investigate the boundary of the
attainable set with the help of the Pontryagin maximum principle for the
time-optimal control problem. We study extremal trajectories that correspond to
bang-bang, singular and mixed controls. We obtain upper bounds for the number
of switchings for optimal controls. This implies a parametrization of the
boundary faces of the attainable set.

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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga