Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of Optimal Solutions and the Optimal Cost for Hybrid
  Dynamical Systems via Reachability Analysis   For a general optimal control problem for dynamical systems with hybrid
dynamics, we study the dependency of the optimal cost and of the value function
on the initial conditions, parameters, and perturbations. We show that upper
and lower semicontinuous dependence of solutions on initial conditions --
properties that are captured by outer and inner well-posedness, respectively --
lead to the existence of a solution to the hybrid optimal control problem and
upper/lower semicontinuity of the optimal cost. In particular, by exploiting
properties of finite horizon reachable sets for hybrid systems, we show that
the optimal cost varies upper semicontinuously when the hybrid system is
(nominally) outer well-posed, and lower semicontinuously when it is (nominally)
inner well-posed and an additional assumption requiring partial knowledge of
solutions. Consequently, when the system is both (nominally) inner and outer
well-posed and the aforementioned assumption holds, the optimal cost varies
continuously, and optimal solutions vary upper semicontinuously. We further
show that even in the absence of this solution-based assumption, the optimal
cost can be continuously approximated. The results are demonstrated in finite
horizon optimization problems with hybrid dynamics, both theoretically and
numerically.

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom