Adams–Bashforth-Type Discrete-Time Zeroing Neural Networks Solving Time-Varying Complex Sylvester Equation With Enhanced Robustness

Abstract

In this article, two Adams–Bashforth-type integration-enhanced discrete-time zeroing neural dynamic (ADTIZD) models are proposed to solve the time-varying complex Sylvester equation (TVCSE) problem in the first time. In ADTIZD models, Adams–Bashforth discrete formulas as novel discrete formulas are used, giving our ADTIZD models higher accuracy [truncation error being <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(\tau ^{5})$ </tex-math></inline-formula> ] but less time and space complexity than the ordinary multi-instant models. Enhanced by the integration part, the ADTIZD models can resist large additive noises, where even constant noises cannot decrease their precision. All convergence and robustness performance conclusions about our ADTIZD models are supported by rigorous theoretical proofs and numerical experiments. More comparisons between ADTIZD models and other discrete-time zeroing neural network models are shown in these experiments too. The efficacy of ADTIZD models is finally been validated in the simulation of adopting them in controlling a robotic manipulator.