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Issue ESAIM: COCV Volume 10, Number 2, April 2004 Page(s) 271 - 294 DOI 10.1051/cocv:2004007

ESAIM: COCV, April 2004, Vol. 10, pp. 271-294
DOI: 10.1051/cocv:2004007

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Fabio Bagagiolo

Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo-Trento, Italy; bagagiol@science.unitn.it.

(Received September 4, 2002. Revised November 4, 2003.)

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.

Mathematics Subject Classification. 47J40, 49J15, 49L20, 49L25.

Key words: Hysteresis, optimal control, dynamic programming, viscosity solutions.


© EDP Sciences, SMAI 2004

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