Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

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

Received: 4 September 2002
Revised: 4 November 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.