Time delay system identification using controlled recurrent neural network and discrete bayesian optimization

Deep learning methods have been widely studied in system modeling due to their strong abilities in feature representation and function fitting. However, most deep learning models are end-to-end black box models, and some key information of the system (such as time delay) cannot be obtained. This paper proposes a grey box model that combines discrete bayesian optimization (DBO) and controlled recurrent neural network (CRNN), namely CRNN-DBO model, aiming at modeling and time delay identification for time delay systems. CRNN is introduced and learns to map the relationship between input data and output data by backpropagation algorithm, while the unknown time delays are modeled as hyperparameters of the mask layer in the CRNN model which are identified by DBO method. The backpropagation algorithm and the DBO method are combined to find the minimal loss value of the model, and the correct time delays as well. To ensure the convergence of the DBO method, l2 regularization term of the mask layer is added in the loss function. The effectiveness and robustness of the model are verified through simulation in the situations of short time delay, long time delay, and nonlinear time delay system. The results indicate that time delays are accurately identified, and the prediction error is smaller than other models.