Reference modification for trajectory tracking using hybrid offline and online neural networks learning

In this paper, we propose a hybrid offline/online neural networks learning method, which combines complementary advantages of two types of neural networks (NNs): deep NN (DNN) and single-layer radial basis function NN (RBFNN). Firstly, after analyzing the mechatronic system’s model, we select reasonable features as the input of the DNN to learn the inverse dynamic characteristics of the closed-loop system offline, so as to establish the mapping between the desired trajectory and the reference trajectory of the system. The trained DNN is used to generate a new reference trajectory and compensate for the tracking error in advance, which can speed up the convergence of online learning control based on RBFNN. This reference trajectory is further modified iteratively when the tracking task is repeated. For this purpose, a single-layer RBFNN model is established, and an online learning algorithm is developed to update the RBFNN parameters. The proposed hybrid offline/online NN method can improve the tracking performance of mechatronic systems by modifying the reference trajectory on top of the baseline controller without affecting the system stability. To verify the effectiveness of this method, we conduct experiments on a piezoelectric drive platform.