Nonlinear dynamic modeling with Neural Networks

Nonlinear dynamic system modeling is an active research field where several challenges still need to be solved. In particular, capturing both the nonlinear behavior and the dynamics of an unknown system represents a difficult identification problem. On one hand, many different model structures have been proposed within the system identification area to characterize nonlinear dynamic systems (e.g. Volterra kernels, NARX models, block structures and nonlinear state-space models. On the other hand, there has been an increasing attention towards techniques developed in other fields, in particular in the machine learning community, where Neural Networks (NNs) and Support Vector Machines (SVMs) allow one to accurately approximate nonlinear functions. There, a big challenge is how to incorporate dynamics in methods that are essentially designed to model static nonlinearities. To address these issues, we have recently proposed a NN-based technique for the identification of nonlinear state-space (NLSS) models to combine the best of these two worlds.