Zeroing neural network based on the equation AXA = A

Abstract

According to available scientific research, there is no information that Zeroing Neural Network (ZNN) models for calculating the matrix inverse and generalized inverses have been studied on the basis of Penrose equations. Our intention is to present a new ZNN design which defined on the Penrose matrix equations and whose intention is to find the time-variant matrix inverse and pseudoinverse. We propose a novel Zeroing function (ZF) based on the first Penrose equation $AXA=A$. The initiated ZNN design for computing the time-varying inverse and the pseudoinverse is defined and investigated. An explicit form of the defined model is also proposed. The convergence properties of the proposed explicit dynamics are investigated in both the time-invariant and time-varying case. Illustrative simulation results are given in order to verify the obtained theoretical results.