Fuzzy Modeling Using Generalized Neural Networks Kalman Filter Algorithm

Jyh-Shing R. Jang

We propose a new approach to build a fuzzy inference system of which the parameters can be updated to achieve a desired input-output mapping. The structure of the proposed fuzzy inference system is called generalized neural networks, and its learning procedure (rules to update parameters) is basically composed of a gradient descent algorithm and Kalman filter algorithm. Specifically, we first introduce the concept of generalized neural networks (GNN’s) and develop a gradient-descent-based supervised learning procedure to update the GNN’s parameters. Secondly, we observe that if the overall output of a GNN is a linear combination of some of its parameters, then these parameters can be identified by one-time application of Kalman filter algorithm to minimize the squared error. According to the simulation results, it is concluded that the proposed new fuzzy inference system can not only incorporate prior knowledge about the original system but also fine-tune the membership functions of the fuzzy rules as the training data set varies.

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