Analysis on Proper Clustering Structure Fuzzy Controllers

Fuzzy controller designing approaches are represented by TSK fuzzy models. Traditional structure learning algorithms are to adjust the parameters in the fuzzy rules based on modeling error. Such an approach will result an improper clustering structure, especially, when the training data are corrupted with outliers. Such a controller is called improper clustering structure fuzzy controllers (IPFC). The paper proposes a way of designing controllers with proper clustering structure (PFC) for affine TSK fuzzy models directly from training data, which may contain noise and outliers. Based on the Lyapunov theorem, an instability sufficient condition for modeling-error bound is derived. Furthermore, the adaptive law to tune the parameters of consequent parts is also obtained. Various simulations are conducted and the results verify that the PFC indeed showed superior performance over other IPFCs.