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viscositysolutions.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Viscosity solutions for an optimal control problemwith Preisach hysteresis nonlinearities
Fabio Bagagiolo
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 2 / April 2004

Published online by Cambridge University Press:

15 March 2004, pp. 271-294

Print publication:

April 2004
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We study a finite horizon problem for a system whose evolution isgoverned by a controlled ordinary differential equation, which takesalso account of a hysteretic component: namely, the outputof a Preisach operator of hysteresis. We derive a discontinuousinfinitedimensional Hamilton–Jacobi equation and prove that, under fairlygeneral hypotheses, the value function is the unique bounded anduniformly continuous viscosity solution of the corresponding Cauchyproblem.