Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang-Baxter-like Matrix Equation

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang-Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.

Automated summary

This research introduces three novel zeroing neural network models for addressing the time-varying Yang-Baxter-like matrix equation with arbitrary real time-varying input matrices. These models demonstrate effective performance in dealing with the TV-YBLME.