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.
Keywords: hysteresis, optimal control, dynamic programming, viscosity solutions
@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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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, Volume 10 (2004) no. 2, pp. 271-294. doi : 10.1051/cocv:2004007. http://archive.numdam.org/articles/10.1051/cocv:2004007/
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