Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inner approximations of the region of attraction for polynomial
  dynamical systems   In a previous work we developed a convex infinite dimensional linear
programming (LP) approach to approximating the region of attraction (ROA) of
polynomial dynamical systems subject to compact basic semialgebraic state
constraints. Finite dimensional relaxations to the infinite-dimensional LP lead
to a truncated moment problem in the primal and a polynomial sum-of-squares
problem in the dual. This primal-dual linear matrix inequality (LMI) problem
can be solved numerically with standard semidefinite programming solvers,
producing a hierarchy of outer (i.e. exterior) approximations of the ROA by
polynomial sublevel sets, with a guarantee of almost uniform and set-wise
convergence. In this companion paper, we show that our approach is flexible
enough to be modified so as to generate a hierarchy of polynomial inner
(i.e.\,interior) approximations of the ROA with similar convergence guarantees.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th