Hierarchical Fuzzy CMAC for Nonlinear Systems Modeling

Since the fuzzy cerebellar model articulation controller (FCMAC) uses linguistic variables, it is highly intuitive and easily comprehended. Despite the FCMAC´s good local generalization capability for approximating nonlinear functions and fast learning, a normal FCMAC requires huge memory, and its dimension increases exponentially with the number of inputs. In order to overcome the memory explosion problem, this paper proposes two types of hierarchical FCMAC (HFCMAC). Another contribution of the paper is that we give stable learning algorithms for these two HFCMACs. Backpropagation-like approach is applied to train each block with a time-varying learning rate, which is obtained by the input-to-state stability technique.