A super-twisting algorithm combined zeroing neural network with noise tolerance and finite-time convergence for solving time-variant Sylvester equation

Abstract

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).