Geodesic
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

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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.

DOI : 10.1051/cocv:2004007
Classification : 47J40, 49J15, 49L20, 49L25
Keywords: hysteresis, optimal control, dynamic programming, viscosity solutions 
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     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/}
}
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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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