Kullback-Leibler divergence-based optimal compression of Preisach operator in hysteresis modeling

The Preisach operator is a popular hysteresis model that has been widely applied in magnetic and smart material systems. Fidelity of the model hinges on accurate representation of the Preisach density function on the Preisach plane, which weighs basic hysteretic elements comprising the operator. Parameter identification and control methods for Preisach operators involve the discretization of the Preisach density function, and existing work has typically adopted some predefined discretization scheme, the performance of which could be far from optimal. In this paper we propose a novel scheme for optimal compression of a Preisach operator. The Kullback-Leibler (KL) divergence is utilized to measure the information loss in approximating the Preisach density as piecewise-constant functions. The proposed approach is applied to the modeling of the hysteretic relationship between resistance and temperature of a vanadium dioxide (VO₂) film, and its effectiveness is further examined in open-loop inverse compensation experiments. In particular, under the same complexity constraint, the KL-divergence based Preisach density function discretization scheme results in an inversion error that is only 40% of that under a scheme.