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Viscosity solutions for an optimal control problemwith Preisach hysteresis nonlinearities

Published online by Cambridge University Press:  15 March 2004

Fabio Bagagiolo
Fabio Bagagiolo*
Affiliation:
Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo-Trento, Italy; [email protected].
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Abstract

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.

Keywords

Hysteresisoptimal controldynamic programmingviscositysolutions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 2 , April 2004 , pp. 271 - 294
Copyright
© EDP Sciences, SMAI, 2004

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