NEW FUZZY LEARNING-MODEL WITH RECURSIVE ESTIMATION FOR DYNAMIC-SYSTEMS

A systematic design technique for a discrete-time self-learning fuzzy model, based on fuzzy relational equations, is presented with some novel features. Firstly, the model utilizes a probabilistic fuzzy relation obtained from referential fuzzy sets on the input and output spaces. Secondly, the conventional input-output formulation of the fuzzy relation is extended by introducing internal fuzzy states in order to model the internal dynamics of the given dynamic system. Thirdly, the fuzzy relation is used to estimate the output as a response to a given stimulus by means of the compositional rule of inference extended to include recursive estimation of the internal fuzzy state. As a result, the new model is shown to be a fuzzy automaton. First and second-order versions of the fuzzy model are validated by means of a well-known set of industrial data.