Design and Validation of Zeroing Neural Network With Active Noise Rejection Capability for Time‐Varying Problems Solving

ABSTRACT Recently, the zeroing neural network (ZNN) has demonstrated remarkable effectiveness in tackling time‐varying problems, delivering robust performance across both noise‐free and noisy environments. However, existing ZNN models are limited in their ability to actively suppress noise, which constrains their robustness and precision in solving time‐varying problems. This paper introduces a novel active noise rejection ZNN (ANR‐ZNN) design that enhances noise suppression by integrating computational error dynamics and harmonic behaviour. Through rigorous theoretical analysis, we demonstrate that the proposed ANR‐ZNN maintains robust convergence in computational error performance under environmental noise. As a case study, the ANR‐ZNN model is specifically applied to time‐varying matrix inversion. Comprehensive computer simulations and robotic experiments further validate the ANR‐ZNN's effectiveness, emphasising the proposed design's superiority and potential for solving time‐varying problems.