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Viscosity solutions for an optimal control problem with 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; bagagiol@science.unitn.it.
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Abstract

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

Hysteresisoptimal controldynamic programmingviscosity solutions.
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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