Design and Analysis of Two Nonlinear ZNN Models for Matrix LR and QR Factorization With Application to 3-D Moving Target Location

Abstract

Two nonlinear zeroing neural network (ZNN) models with prescribed-time convergence for time-dependent matrix LR and QR factorization are proposed in this paper. To do so, two algorithms and two error functions are constructed to transform the time-dependent matrix LR and QR factorization problems into time-dependent linear equation systems, respectively. Simultaneously, a new activation function is introduced based on the initial ZNN models for the prescribed-time convergence of models. The excellent performance (robustness and convergence) of the two proposed ZNN models are analyzed theoretically. Furthermore, the prescribed-time convergence and anti-noise abilities of the proposed ZNN models are well demonstrated in numerical experiments. Finally, the proposed ZNN model is applied to the moving target location problem, and the results show that the location error is at the millimeter level.