Artificial neural network hysteresis operators for the identification of Hammerstein hysteretic systems

This paper introduces explicit neural representations of fundamental hysteresis operators such as the play and stop operators. The hysteresis neurons are represented by recurrent artificial neural networks (ANN) using classical activation functions and are trained with gradient-based learning algorithms. The hysteresis neurons are combined into a single ANN hysteretic layer which, from a mathematical point of view, is equivalent to a classical Prandtl-Ishlinskii model expression, but has all the advantages of ANNs. One such benefit is the flexibility it offers to be combined with other ANN layers to obtain various complex model structures. In this paper, this is illustrated by combining it with a linear recurrent neural network to obtain a Hammerstein model structure, which is often considered for the characterization of systems driven by a class of smart material-based actuators. The input nonlinearity in the Hammerstein model is represented by a Prandtl-Ishlinskii ANN hysteretic layer while the linear dynamics are captured using a linear recurrent ANN representing a single-input multiple-output linear time-invariant state-space model. The identification approach of the Hammerstein model with a hysteretic layer is illustrated both numerically and experimentally.