Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities
Dipartimento di Matematica, Università di Trento,
Via Sommarive 14, 38050 Povo-Trento, Italy; firstname.lastname@example.org.
Revised: 4 November 2003
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