Neural Network Algorithms For Solving Generalized Inverse Of Matrices And Time-varying Linear Equations And Inequalities Systems

In modern scientific technology and engineering applications,Moore-Penrose in-verse of full-rank matrices and time-varying linear equations and inequalities systems calculation problems are often involved.The traditional numerical algorithms possess-ing serial schemes are inefficient when they applied to large-scale and time-varying problems,which makes the solving process time-consuming.Therefore,in this paper we propose two more efficient recurrent neural network models for solving the Moore-Penrose inverse of full-rank matrices and time-varying linear equations and inequalities systems,respectively.Motivated by zeroing neural network(ZNN)models,Lv et al.recently proposed two novel neural network(NNN)models for solving Moore-Penrose inverse of a time-invariant full-rank matrix.In this study,we extend the NNN models to more general cases by introducing a "regularization" parameter and a power parameter in these two matrix factors.The proposed models are named as improved recurrent neural network(IMRNN)models since their convergence performance can be much better than NNN models by appropriate choices of the introduced parameters.Such convergence prop-erty is theoretically analyzed in detail.Three numerical experiments are 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.Xu et al.solved a class of time-varying linear equations and inequalities systems by using original ZNN model through introducing a nonnegative relaxation parame-ter vector.However,the introduction of this unknown nonnegative slack vector will increases the model’s size and complexity,and thereby may increase the cost of com-putation.In this study,we propose a variant zeroing neural network model(called VZNN model)in which no additional relaxation parameter vectors are needed.The convergence analysis of the model is performed,and a numerical experiment is given to illustrate VZNN model’s efficiency and effectiveness for solving time-varying linear equations and inequalities systems.Furthermore,the VZNN model is successfully em-ployed to a six-link robot manipulator with limits,which shows the applicability of our model.