Noise-resistant predefined-time convergent ZNN models for dynamic least squares and multi-agent systems

Abstract

Zeroing neural networks (ZNNs) are commonly used for dynamic matrix equations, but their performance under numerically unstable conditions has not been thoroughly explored, especially in situations involving unequal row-column matrices. The challenge is further aggravated by noise, particularly in dynamic least squares (DLS) problems. To address these issues, we propose the QR decomposition-driven noise-resistant ZNN (QRDN-ZNN) model, specifically designed for DLS problems. By integrating QR decomposition into the ZNN framework, QRDN-ZNN enhances numerical stability and guarantees both precise and rapid convergence through a novel activation function (N-Af). As validated by theoretical analysis and experiments, the model can effectively counter disturbances and enhance solution accuracy in dynamic environments. Experimental results show that, in terms of noise resistance, the QRDN-ZNN model outperforms existing mainstream ZNN models, including the original ZNN, integral-enhanced ZNN, double-integral enhanced ZNN, and super-twisting ZNN. Furthermore, the N-Af offers higher accuracy and faster convergence than other state-of-the-art activation functions. To demonstrate the practical utility of the method, We develop a new noise-resistant consensus protocol inspired by QRDN-ZNN, which enables multi-agent systems to reach consensus even in noisy conditions.