Nonlinear function activated GNN versus ZNN for online solution of general linear matrix equations

Abstract

In this work, the gradient-based design method is generalized to establish a finite-/fixed-time GNN (gradient-based neural network) to obtain an online solution of the general linear matrix equation (LME): P1X(t)Q1+P2X(t)Q2=G. Two nonlinear activation functions (AFs), which are broadly investigated in ZNN (zeroing neural network), are introduced and put to use for the construction of the GNN model. Theoretical analyses and comparisons are given to illustrate their impacts on the GNN and the corresponding ZNN models in terms of convergence. It is shown that both the GNN model and the ZNN model exhibit the same convergence property (i.e., finite-/fixed-time convergence) under the action of the same AF. A tighter estimate of the upper bound of fixed convergence time is also obtained for the ZNN model. Comparative verification is conducted to confirm the validation of theoretical analysis.