Adaptive fuzzy modeling of nonlinear dynamical systems
The paper proposes an analytical approach for a fuzzy model of a multivariate discrete-time nonlinear dynamical system. In this model, the conventional differential equation is replaced by a set of fuzzy rules and corresponding membership functions. According to the authors, this approach is justified by the high degree of complexity of the problem, due to which a high precision becomes irrelevant for most applications. The model is framed around the concepts of fuzzy quantization, fuzzy variables and rules, fuzzification and defuzzification procedures. Further characteristics of the model are its compactness, the requirement to be excitation-dependent and the necessity to work on-line. The paper provides a convincing convergence analysis and illustrates the approach by a well chosen example, visualized by means of figures and graphs. The particular fuzzy model structure developed in the paper may serve for the development of a rigorous fuzzy system theory and provide the fuzzy control designers with systematic and justifiable design techniques.
scientific article; zbMATH DE number 885876