Optimal Compression of a Generalized Prandtl-Ishlinskii Operator in Hysteresis Modeling

The Prandtl-Ishlinskii (PI) model is a popular hysteresis model that has been widely applied in smart materials-based systems. Recently, a generalized PI model is formulated that is capable of characterizing asymmetric, saturated hysteresis. The fidelity of the model hinges on accurate representation of envelope functions, play operator radii, and corresponding weights. For a given number of play operators, existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes based on entropy and relative entropy (Kullback-Leibler divergence) for optimal compression of a generalized PI model are proposed to best represent the original hysteresis model subject to a given complexity constraint, i.e., the number of play operators. The overall compression performance is expressed as a cost function, and is optimized using dynamic programming. The proposed compression schemes are applied to the modeling of the asymmetric hysteresis between resistance and temperature of a vanadium dioxide (VO₂) film, and the effectiveness is further demonstrated in a model verification experiment. In particular, under the same complexity constraint, an entropy-based compression scheme and a Kullback-Leibler divergence-based compression scheme result in modeling errors around 37% and 48%, respectively, of that under a uniform compression scheme.