Generalized backpropagation through time for continuous-time neural models identification

Dynamical neural networks are frequently used as models of complex systems. Backpropagation Through Time (BPTT) is a standard technique for dynamical (recurrent) neural networks learning. It depends on "unfolding" in time of the original recurrent neural network and application of the classic backpropagation algorithm. There are similar approaches known in the literature avoiding the unfolding in time which may be very complicated for some neural-based models. Recently we propose the Generalized Backpropagation Through Time (GBPTT) algorithm for continuous-time neural networks identification based on discrete-time measurements. Here we present the proof of the correctness of the method.