An Amplitude Activation Function-Based Model for Behavioral Modeling of Nonlinear Systems

Nonlinear models with a linear-in-coefficients property, i.e., the property that the model output is linear with respect to model coefficients, are highly valuable for behavioral modeling of nonlinear systems. One major reason is that well-established estimation methods used in linear systems (such as the least-squares estimation) are suitable for model identification. To date, however, nonlinear models with a linear-in-coefficients property have been limited almost exclusively to polynomial function-based models. This paper explores the use of nonlinear functions other than the polynomial function to construct a nonlinear model that maintains the linear-in-coefficients property. Specifically, a new linear-in-coefficients model structure is proposed, which generates a model basis function from any typical nonlinear function. The nonlinear function used to construct the proposed model is comparable to the activation function of the neural network. It can be, e.g., the exponential function, the logarithmic function, or even the ReLU function. Therefore, the proposed model is called an amplitude activation function (AAF)-based model. The proposed AAF-based model introduces several slope and intercept factors to generate different basis functions. Its memory structure draws on that of the conventional polynomial function-based model. Experiments demonstrate that the proposed AAF-based model is more robust to the number of training samples compared with the conventional polynomial function-based model.