A Hammerstein Recurrent Neurofuzzy Network With an Online Minimal Realization Learning Algorithm

This paper presents a Hammerstein recurrent neurofuzzy network associated with an online minimal realization learning algorithm for dealing with nonlinear dynamic applications. We fuse the concept of states in linear systems into a neurofuzzy framework so that the whole structure can be expressed by a state-space representation. An online minimal realization learning algorithm has been developed to find a controllable and observable state-space model of minimal size from the input-output measurements of a given system. Such an idea can simultaneously resolve the problem of the determination of a minimal structure and the difficulty of network stability analysis. The advantages of our approach include: 1) our recurrent network is capable of translating the complicated dynamic behavior of a nonlinear system into a minimal set of linguistic fuzzy dynamical rules and into state-space representation as well and 2) an online minimal realization learning algorithm unifies an order determination algorithm, a hybrid parameter initialization method, and a recursive recurrent learning algorithm into a systematic procedure to identify a minimal structure with satisfactory performance. Performance evaluations on benchmark examples as well as real-world applications have successfully validated the effectiveness of our approach.