Integration enhanced and noise tolerant ZNN for computing various expressions involving outer inverses

An integration-enhanced noise-tolerant zeroing neural network (IENTZNN) model for computing various expressions involving outer inverses is defined and considered. The model assumes an input matrix A, two appropriately selected matrices F, G, a regularization parameter, and will be shortly denoted by IENTZNN(A, F, G). Particularly, IENTZNN(A, F, G) is applicable in computing real-time-varying matrix outer inverse with prescribed range and null space under the presence of various kinds of noises. The model is an extension of the IEZNN model for solving the problem of real-time matrix inversion as well as an integration-enhanced and noise-tolerant extension of the ZNNATS2 model for approximating time-varying outer inverse with prescribed range and null space. Theoretical analyses show that the proposed integration-enhanced model globally and exponentially converges to the theoretical solution. Moreover, the proposed IENTZNN(A, F, G) model is proven to have a very good performance in the presence of various kinds of noise. Finally, illustrative simulation examples are presented to testify the efficacy of the proposed model.