Neural networks based model for systems with input hysteresis

A method for modeling of the linear dynamic systems with input hysteresis is proposed. Considering hysteresis involved in the system is a non-smooth and multi-valued nonlinearity, the generalized gradient of the output with respect to the input of the nonlinear system is introduced to extract the movement tendency of the system. Then, the generalized gradient is included into the expanded input space, which realizes the transformation of the multi-valued mapping of the linear system with input hysteresis into a one-to-one mapping. In this case, the neural networks can be applied to the approximation of the systems. Finally, a numerical example is illustrated to show the modeling performance of the proposed approach.