Multistep Prediction of Dynamic Systems With Recurrent Neural Networks.

In this paper, we address the state initialization problem in recurrent neural networks (RNNs), which seeks proper values for the RNN initial states at the beginning of a prediction interval. The proposed methods employ various forms of neural networks (NNs) to generate proper initial state values for RNNs. A variety of RNNs are trained using the proposed NN initialization schemes for modeling two aerial vehicles, a helicopter and a quadrotor, from experimental data. It is shown that the RNN initialized by the NN-based initialization method outperforms the washout method which is commonly used to initialize RNNs. Furthermore, a comprehensive study of RNNs trained for multistep prediction of the two aerial vehicles is presented. The multistep prediction of the quadrotor is enhanced using a hybrid model, which combines a simplified physics-based motion model of the vehicle with RNNs. While the maximum translational and rotational velocities in the Quadrotor data set are about 4 m/s and 3.8 rad/s, respectively, the hybrid model produces predictions, over 1.9 s, which remain within 9 cm/s and 0.12 rad/s of the measured translational and rotational velocities, with 99% confidence on the test data set.