Trainable Delays in Time Delay Neural Networks for Learning Delayed Dynamics

In this article, the connection between time delay systems and time delay neural networks (TDNNs) is presented from a continuous-time perspective. TDNNs are utilized to learn the nonlinear dynamics of time delay systems from trajectory data. The concept of TDNN with trainable delay (TrTDNN) is established, and training algorithms are constructed for learning the time delays and the nonlinearities simultaneously. The proposed techniques are tested on learning the dynamics of autonomous systems from simulation data and on learning the delayed longitudinal dynamics of a connected automated vehicle (CAV) from real experimental data.