Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reachability for Partially Observable Discrete Time Stochastic Hybrid
  Systems   When designing optimal controllers for any system, it is often the case that
the true state of the system is unknown to the controller, for example due to
noisy measurements or partially observable states. Incomplete state information
must be taken into account in the controller's design in order to preserve its
optimality. The same is true when performing reachability calculations. To
estimate the probability that the state of a stochastic system reaches, or
stays within, some set of interest in a given time horizon, it is necessary to
find a controller (or at least prove one exists) that drives the system to that
set with maximum probability. This controller, however, does not have access to
the true state of the system. To date, little work has been done on stochastic
reachability calculations with partially observable states. What work has been
done relies on converting the reachability optimization problem to one with an
additive cost function, for which theoretical results are well known. Our
approach is to preserve the multiplicative cost structure when deriving a
sufficient statistic that reduces the problem to one of perfect state
information. Our transformation includes a change of measure that simplifies
the distribution of the sufficient statistic conditioned on its previous value.
We develop a dynamic programming recursion for the solution of the equivalent
perfect information problem, proving that the recursion is valid, an optimal
solution exists, and results in the same solution as to the original problem.
We also show that our results are equivalent to those for the reformulated
additive cost problem, and so such a reformulation is not required.

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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: physics