A New Approach in Fuzzy Adaptive Filtering

Abstract

A new fuzzy adaptive filter using Lyapunov stability theory is proposed in this paper. This fuzzy adaptive filter is constructed from a set of changeable fuzzy IF-THEN rules. The adaptive algorithm, Lyapunov theory-based adaptive filtering (LAF) is used to update the parameter of the membership functions so that the dynamic error between the filter output and the desired response converges to zero asymptotically. Therefore, the most advantage of the fuzzy filter compared to the conventional filters is that linguistic information from human experts (in the form of fuzzy IF-THEN rules) can be incorporated into the filter. If no linguistic information is available, the fuzzy adaptive filters become well-defined nonlinear adaptive filters. The stability of the fuzzy adaptive filter is guaranteed by Lyapunov theory, thus the filter is highly stable. The design of the fuzzy filter is independent of signal stochastic’ properties. Simulation examples of fuzzy adaptive filter are performed to support the theoretical results.