Intelligent modeling for hysteresis nonlinearity

It is known that hysteresis is a non-differentiable nonlinearity with multi-value mapping. The neural networks, however, can only be applied to modeling the function with one-to-one mapping. Under a mild assumption, this paper obtains a theorem to derive an invertable mapping between the coordinate related to a certain Preisach model and the integral interface that is the key element in Preisach model. Then it proves that there exists a mapping, which can describe hysteresis nonlinearity and be implemented easily by neural networks.