Improved recurrent neural networks for solving Moore-Penrose inverse of real-time full-rank matrix

Abstract

Recently, motivated by Zhang neural network (ZNN) models, Lv et al. presented two novel neural network (NNN) models for solving Moore-Penrose inverse of a time-invariant full-rank matrix. The NNN models were established by introducing two new matrix factors in the ZNN models, which results in their higher convergence rates than those of the ZNN models. In this paper we extend the NNN models to the more general cases through introducing a “regularization” parameter and a power parameter in these two matrix factors. The new proposed models are named here as the improved recurrent neural networks (IMRNN) since their convergence performance can be much better than the NNN models by appropriate choices of the introduced parameters. Such convergence property is theoretically analyzed in detail. Some numerical experiments are also performed to validate the theoretical results, including the numerical comparisons with the existing gradient neural network (GNN), ZNN and NNN models. In particular, the proposed IMRNN models are successfully applied to the inverse kinematic control of a three-link redundant robot manipulator where the superiority of the IMRNN models to the GNN, ZNN and NNN models is also indicated.