Application of Two Fuzzy Logic Systems to Complex-Type ZNN Models for the Drazin Inverse of Time-Dependent Complex-Value Matrix

Abstract

In accordance with the advantages of zeroing neural network (ZNN) with the parallel processing character and fuzzy logic systems for calculating the uncertainties, two complex-type fuzzy ZNN (CtFZNN) models, which are mainly derived from two different limit forms of the Drazin inverse, are developed for solving the time-dependent complex-value Drazin inversion (TDCVDI) problem in this article. The most significant feature of the CtFZNN models is to use the improved fuzzy evolutionary formula, where the traditional constant or time-dependent factors are replaced by the fuzzy factors. For the non-noise or the noise disturbed CtFZNN models, the applied fuzzy factors are, respectively, generated from the single-input and single-output fuzzy logic system or the double-input and single-output fuzzy logic system. From the analytical discussions, it can conclude that the proposed CtFZNN models not only have finite-time convergence and inherent noise tolerance simultaneously, but also possess faster adaptive convergence rate even in a noisy environment. The presented theorems and the provided numerical simulations demonstrate the effectiveness of the proposed methods for addressing the TDCVDI problem, especially compared to the general ZNN model.