Continuous-time nonlinear signal processing: a neural network based approach for gray box identification

Artificial neural networks (ANNs) are often used for short term discrete time series predictions. Continuous-time models are, however, required for qualitatively correct approximations to long-term dynamics (attractors) of nonlinear dynamical systems and their transitions (bifurcations) as system parameters are varied. In previous work the authors developed a black-box methodology for the characterization of experimental time series as continuous-time models (sets of ordinary differential equations) based on a neural network platform. This methodology naturally lends itself to the identification of partially known first principles dynamic models, and here the authors present its extension to "gray-box" identification.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>