Inverting the Preisach model of hysteresis

The Preisach model describes the output of a hysteretic system in the form of a history-dependent double integral of the Preisach distribution function [1]. Many efficient numerical implementations have been developed in the literature to compute the output as a function of input, however, inverting the Preisach operator (i.e. computing the input variable as a function of the output) remains a difficult task. A number of authors have proven the existence and continuity of the inverse of the Preisach operator [2, 3], however, the lack of efficient numerical algorithms to invert the operator has limited the area of applicability of the model and made it only sporadically used in the real-time control applications involving optimal design, sensors and actuators, smart materials, and other mechanical systems where it is imperative control the output accurately [4,5,6].