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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.
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.
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