System identification using hierarchical fuzzy CMAC neural networks

The conventional fuzzy CMAC can be viewed as a basis function network with supervised learning, and performs well in terms of its fast learning speed and local generalization capability for approximating nonlinear functions. However,it requires an enormous memory and the dimension increase exponentially with the input number. Hierarchical fuzzy CMAC (HFCMAC) can use less memory to model nonlinear system with high accuracy. But the structure is very complex, the normal training for hierarchical fuzzy CMAC is difficult to realize. In this paper a new learning scheme is employed to HFCMAC. A time-varying learning rate assures the learning algorithm is stable. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds. The new algorithms are very simple, we can even train each sub-block of the hierarchical fuzzy neural networks independently.