Identification and inversion of smooth hysteretic maps

This article introduces straightforward techniques for modeling, identification and inversion of a class of hysteretic systems. The assumed model structure consists of the parametric hysteresis operator and an input or output shaping function. The parametric hysteresis operator isolates the most general multi-valued hysteretic behavior in a well-defined operator form, while the remaining bijective shaping function models all other single valued non-linearities. The emphasis of this article is on the identification of quasi-static maps of such systems using specific input signals and data measured at the output.