Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: State constrained control problems in Banach lattices and applications   This paper aims to study a family of deterministic optimal control problems
in infinite dimensional spaces. The peculiar feature of such problems is the
presence of a positivity state constraint, which often arises in economic
applications. To deal with such constraints, we set up the problem in a Banach
space with a Riesz space structure (i.e., a Banach lattice) not necessarily
reflexive: a typical example is the space of continuous functions on a compact
set. In this setting, which seems to be new in this context, we are able to
find explicit solutions to the Hamilton-Jacobi-Bellman (HJB) equation
associated to a suitable auxiliary problem and to write the corresponding
optimal feedback control. Thanks to a type of infinite dimensional
Perron-Frobenius Theorem, we use these results to get information about the
optimal paths of the original problem. This was not possible in the infinite
dimensional setting used in earlier works on this subject, where the state
space was an $\mathrm L^2$ space.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio