Prandtl-Ishlinskii (PI) hysteresis models have been used widely in magnetic and smart material-based systems. A generalized PI model, consisting of a weighted superposition of generalized play operators, is capable of characterizing saturated and asymmetric hysteresis. The fidelity of the model hinges on accurate representation of the envelope functions, play operator radii, and corresponding weights. Existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes are proposed for optimally compressing generalized PI models, subject to a complexity constraint characterized by the number of play operators. An information-theoretic tool, entropy, is adopted to capture the information loss in replacing a group of weighted play operators with a single play operator. The optimal compression algorithm is reformulated as an optimal control problem and solved with dynamic programming, the computational complexity of which is shown to be much lower than that of exhaustive search. Simulation results are first presented to examine the performance of the proposed approach in approximating a PI model consisting of a large number of play operators, where cases with different types of weight distributions are explored. The approach is further applied to compress an experimentally identified generalized PI model for the complex hysteresis behavior between the resistance and temperature of vanadium dioxide, a promising multifunctional material. Both simulation and experimental results demonstrate that the proposed algorithms in general yield far more superior performance than a typically adopted scheme where the play radii are assigned uniformly. (C) 2015 Elsevier Ltd. All rights reserved.