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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. [ABSTRACT FROM AUTHOR]

The time-variant Sylvester equation (TVSE) plays a highly crucial role in many areas of scientific research and engineering applications. Recently, zeroing neural network (ZNN) has been prevailed as an effective solution for time-variant problem. However, the majority of the existing ZNN solution schemes for TVSE are either only considered in noiseless environments or are unable to converge in a finite amount of time, and while there is a pressing need for effective and noise-resisting ZNNs to fulfill real-time applications' requirements in the actual world. For this reason, inspired by the advantages offered by super-twisting algorithm (STA), being a well-accepted second order sliding mode method, this paper introduces STA into ZNN and establishes a novel STZNN model for TVSE solving. Actually, the intrinsic properties of STA, such as finite-time convergence and anti-noise robustness, are perfectly in line with what an efficient and noise-resisting ZNN model desired to be. Hence, the STZNN model can realize a much quick convergence time and a much great resistance against noise. Moreover, rigorous theoretical analyses on the case of zero noise, constant noise and dynamic bounded noise are conducted, and the illustrative verification not only verifies the STZNN's convergence property, validates its superior ability in convergence time and noise resisting compared to the gradient-based neural network (GNN), the conventional ZNN (CZNN) model and the integration-enhanced ZNN (IEZNN) model, but also shows the STZNN model's capability in addressing moving localization problems based on angle of arrival (AoA) and time difference of arrival (TDOA). [ABSTRACT FROM AUTHOR]