On nonconvex differential inclusions whose state is constrained in the closure of an open set. Applications to dynamic programming
type: Item
instance of: scholarly article
title: On nonconvex differential inclusions whose state is constrained in the closure of an open set. Applications to dynamic programming
zbMATH Open document ID: 1015.34006
author: Francesca Forcellini
author: Franco Rampazzo
published in: Differential and Integral Equations
publication date: 2003-01-26T00:00:00Z
review text: The authors present two main results which extend the Filippov theorem to nonconvex differential inclusions with constrained state variable. One involves a mapping \(F\) being Lipschitz in \((t,x)\) and the boundary of the set of state variable constraints \(\Theta \) being locally Lipschitz; the other one requires merely a measurability of \(F\) in \(t\) but the boundary of \(\Theta \) has to be sufficiently smooth. The theorems are applied to prove some continuity properties of the value function for the Boltz problem with state constraints and with the control set depending on both time and state.
reviewed by: David S. Boukal
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J24
zbMATH DE Number: 1858757
zbMATH Keywords: Filippov's theorem
zbMATH Keywords: state constraints
zbMATH Keywords: optimal control
zbMATH Keywords: Boltz problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1858757