We prove, in a Hilbert space setting, that all targets of the minimum norm optimal control problems reachable with inputs of minimum norm ρ are support points for the the set reachable by inputs with norm bounded by ρ. This amount to say that the Maximum Principle always holds in Hilbert Spaces.
@article{1372,
title = {Closure of Pointed Cones and Maximum Principle in Hilbert Spaces},
journal = {CUBO, A Mathematical Journal},
volume = {13},
year = {2011},
language = {en},
url = {http://dml.mathdoc.fr/item/1372}
}
D’alessandro, Paolo. Closure of Pointed Cones and Maximum Principle in Hilbert Spaces. CUBO, A Mathematical Journal, Tome 13 (2011) . http://gdmltest.u-ga.fr/item/1372/