A hybrid learning scheme combining EM and MASMOD algorithms for fuzzy local linearization modeling

Fuzzy local linearization (FLL) is a useful divide-and-conquer method for coping with complex problems such as modeling unknown nonlinear systems from data for state estimation and control. Based on a probabilistic interpretation of FLL, the paper proposes a hybrid learning scheme for FLL modeling, which uses a modified adaptive spline modeling (MASMOD) algorithm to construct the antecedent parts (membership functions) in the FLL model, and an expectation-maximization (EM) algorithm to parameterize the consequent parts (local linear models). The hybrid method not only has an approximation ability as good as most neuro-fuzzy network models, but also produces a parsimonious network structure (gain from MASMOD) and provides covariance information about the model error (gain from EM) which is valuable in applications such as state estimation and control. Numerical examples on nonlinear time-series analysis and nonlinear trajectory estimation using FLL models are presented to validate the derived algorithm.