IDENTIFICATION OF HYSTERETIC CONTROL INFLUENCE OPERATORS REPRESENTINGSMART ACTUATORS PART-I - FORMULATION

A large class of emerging actuation devices and materials exhibit stro ng hysteresis characteristics during their routine operation. For exam ple, when piezoceramic actuators are operated under the influence of s trong electric fields, it is known that the resulting input-output beh avior is hysteretic. Likewise, when shape memory alloys are resistivel y heated to induce phase transformations, the input-output response at the structural level is also known to be strongly hysteretic. This pa per investigates the mathematical issues that arise in identifying a c lass of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically , the identification of a class of distributed hysteresis operators th at arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introd uce distributed, hysteretic control influence operators derived from s moothed Preisach operators and generalized hysteresis operators derive d from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hystereti c control influence operator can bce expressed as an ouput least squar e minimization over probability measures defined on a compact subset o f a closed half-plane. In Part II of this paper, consistent and conver gent approximation methods for identification of the measure character izing the hysteresis are derived.