Zeroing Neural Networks Combined with Gradient for Solving Time-Varying Linear Matrix Equations in Finite Time with Noise Resistance

Due to the time delay and some unavoidable noise factors, obtaining a real-time solution of dynamic time-varying linear matrix equation (LME) problems is of great importance in the scientific and engineering fields. In this paper, based on the philosophy of zeroing neural networks (ZNN), we propose an integration-enhanced combined accelerating zeroing neural network (IEAZNN) model to solve LME problem accurately and efficiently. Different from most of the existing ZNNs research, there are two error functions combined in the IEAZNN model, among which the gradient of the energy function is the first design for the purpose of decreasing the norm-based error to zero and the second one is adding an integral term to resist additive noise. On the strength of novel combination in two error functions, the IEAZNN model is capable of converging in finite time and resisting noise at the same time. Moreover, theoretical proof and numerical verification results show that the IEAZNN model can achieve high accuracy and fast convergence speed in solving time-varying LME problems compared with the conventional ZNN (CZNN) and integration-enhanced ZNN (IEZNN) models, even in various kinds of noise environments.