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 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 gain 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 L2 space.
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|Titolo:||STATE CONSTRAINED CONTROL PROBLEMS IN BANACH LATTICES AND APPLICATIONS|
|Data di pubblicazione:||2021|
|Appare nelle tipologie:||01.01 - Articolo su rivista|