Hysteretic control influence operators representing smart material actuators: identification and approximation

This paper discusses mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling shape memory alloy actuation. Specifically, the identifiability of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. We introduce distributed, hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an output least square minimization over probability measures defined on a compact subset of a closed half-plane