Identification of Dynamical Systems Using Recurrent Neurofuzzy Modeling

Abstract

In this chapter, we analyze the identification problem, which consists of choosing an appropriate identification model and adjusting its parameters according to some adaptive law, such that the response of the model to an input signal (or a class of input signals), approximates the response of the real system for the same input. As identification models, we use fuzzy-recurrent high-order neural networks (F-RHONNs). This model exploits the use of high-order networks (HONN), which are expansions of the first-order Hopfield and Cohen-Grossberg models that allow higher order interactions between neurons. It combines HONN with an underlying fuzzy model of Mamdani type assuming a standard defuzzification procedure such as centroid of area or weighted average. . Learning laws are proposed which ensure that the identification error converges to zero exponentially fast or to a residual set when a modeling error is applied. In the proposed method, there are two core ideas : (1) Several high-order neural networks are specialized to work around fuzzy centers, separating in this way the system in simpler (NF) subsystems with better approximation abilities and (2) the use of a novel method called switching parameter hopping to replace the commonly used $\sigma$-modification for the robustness of our system in order to restrict the weights and avoid drifting of their values to infinity.