Filter Design for Gated Recurrent Unit Neural Networks via a T-S Fuzzy Approach

This paper introduces an effective idea which can easily extend filter design methods of recurrent neural networks (RNNs) to gated recurrent units (GRUs). Although the GRU is widely used in the many applications, its filter design method has not been studied yet. Because the gating mechanism makes the dynamics of the RNNs more complex, existing filter design methods of the RNNs cannot be directly applied to the GRUs. In the proposed method, the TakagiSugeno (T-S) fuzzy model is used to simply reformulate the dynamics of the GRU as the weighted sum of sub-recurrent neural networks, and a filter design method is presented for the fuzzified GRU model. In addition, the mismatched membership function problem of the fuzzy filtering error system is resolved by adopting the transformed membership functions. It has an advantage that the existing relaxation methods of the stabilization criterion can be directly applied to the presented method. The proposed method is verified through a GRU model, and the average root-mean-squared errors for each of the three hidden states are close to zero (0.1130,0.1796,0.1106) for a given three-dimensional numerical problem.