A Zeroing Neural Network Approach for Calculating Time-Varying G-Outer Inverse of Arbitrary Matrix.

Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to tackle TV challenges. This work investigates the challenge of finding a TV extension of a subclass of inner inverses on real matrices, known as generalized-outer (G-outer) inverses. More precisely, our goal is to construct TV G-outer inverses (TV-GOIs) by utilizing the zeroing neural network (ZNN) process, which is presently thought to be a state-of-the-art solution to tackling TV matrix challenges. Using known advantages of ZNN dynamic systems, a novel ZNN model, called ZNNGOI, is presented in the literature for the first time in order to compute TV-GOIs. The ZNNGOI performs excellently in performed numerical simulations and an application on addressing localization problems. In terms of solving linear TV matrix equations, its performance is comparable to that of the standard ZNN model for computing the pseudoinverse.