Identification of nonlinear systems with unknown time delay based on time-delay neural networks

In this letter, we address the problem of online identification of nonlinear continuous-time systems with unknown time delay based on neural networks (NNs). A novel time-delay NN model with learning algorithm is employed to perform simultaneous system identification and time-delay estimation. The proposed network is an extended version of the time-delay-free dynamical NN. Rigorous stability proof for the identification error is given by means of Lyapunov theory. The simulation studies are provided to demonstrate the performance of the identification algorithm and clarify the theoretical implications.