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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton-Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
@article{COCV_2004__10_2_271_0,
author = {Bagagiolo, Fabio},
title = {Viscosity solutions for an optimal control problem with {Preisach} hysteresis nonlinearities},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {271--294},
publisher = {EDP-Sciences},
volume = {10},
number = {2},
year = {2004},
doi = {10.1051/cocv:2004007},
mrnumber = {2083488},
zbl = {1068.49024},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004007/}
}
TY - JOUR AU - Bagagiolo, Fabio TI - Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 271 EP - 294 VL - 10 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004007/ DO - 10.1051/cocv:2004007 LA - en ID - COCV_2004__10_2_271_0 ER -
%0 Journal Article %A Bagagiolo, Fabio %T Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 271-294 %V 10 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004007/ %R 10.1051/cocv:2004007 %G en %F COCV_2004__10_2_271_0
Bagagiolo, Fabio. Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 271-294. doi: 10.1051/cocv:2004007
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