Fuzzy modeling: an adaptive approach

Fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. We start by developing a proper framework based on the key notions of fuzzy quantization and function approximation. This framework allows the fuzzy modeling to be justified with mathematical rigor, and the modeling problem be formulated in a way suitable for an analytical solution. Based on the formulation, an online scheme is developed that adaptively forms the fuzzy model from samples of a dynamical system by generating and modifying a set of fuzzy rules and membership functions. The convergence analysis of the scheme is carried out rigorously based on the Lyapunov theory, and the major convergence result is established. The scheme is also applied to a few nonlinear modeling problems to demonstrate its feasibility and effectiveness