Noise-tolerant Neural Network For Time-varying Matrix Pseudoinversion

Computational problems such as matrix algebra,vector algebra and opti-mization are widely encountered in the fields of science,engineering and socioe-conomics.Moreover,such computational problems usually need to be solved in real time or online,which may be referred to as real-time(mathematical)computational problems.This paper focuses on real-time(mathematical)com-putational problems in the presence of external interference and noise inter-ference,and proposes a novel Zeroing neural network model(Noise-tolerant Continuous-time Zeroing Neural Network,NTCTZNN),which can accurate-ly and effectively solve the time-varying pseudoinverse of the matrix in real time under the conditions of various noise pollution via detailed theoretical analysis and proof.Moreover,the theoretical results show that the network model not only has the superior convergence performance,but also has a good noise-tolerant performance.In addition,in order to achieve the purpose of hardware implementation,by using the forward difference formula to discretize the NTCTZNN model,a noise-tolerant discrete-time Zeroing neural network(NTDTZNN)model is proposed and studied for the time-varying matrix pseu-doinversion in various noisy environments.Its stability and convergence are also proved by theory.For comparative purposes,the conventional Zeroing neural network and gradient-based neural networks are also used to solve the same problems.The numerical simulation results confirm the effectiveness and supe-riority of the noise-tolerant Zeroing neural network model and the discrete-time noise-tolerant Zeroing neural network model for time-varying matrix pseudoin-version in the presence of various types of noise.