Abstract

The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is deliberately developed and analyzed for a time-varying Lyapunov equation, which inherits the exponential convergence rate of the classical CTZNN in a noiseless environment. Theoretical results show that for a time-varying Lyapunov equation with constant noise or time-varying linear noise, the proposed NTCTZNN model is convergent, no matter how large the noise is. For a time-varying Lyapunov equation with quadratic noise, the proposed NTCTZNN model converges to a constant which is reciprocal to the design parameter. These results indicate that the proposed NTCTZNN model has a stronger anti-noise capability than the traditional CTZNN. Beyond that, for potential digital hardware realization, the discrete-time version of the NTCTZNN model (NTDTZNN) is proposed on the basis of the Euler forward difference. Lastly, the efficacy and accuracy of the proposed NTCTZNN and NTDTZNN models are illustrated by some numerical examples.

中文翻译：

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时变Lyapunov方程的新型耐张张神经网络。

摘要

张神经网络（ZNN）已成为解决各种时变问题的基准解决方案。本文利用新颖的设计公式，针对时变的Lyapunov方程，专门开发并分析了耐噪声连续时间ZNN（NTCTZNN）模型，该模型继承了经典CTZNN在无噪声环境中的指数收敛速度。理论结果表明，对于具有恒定噪声或时变线性噪声的时变Lyapunov方程，无论噪声有多大，提出的NTCTZNN模型都是收敛的。对于具有二次噪声的时变Lyapunov方程，提出的NTCTZNN模型收敛到一个常数，该常数与设计参数成反比。这些结果表明，所提出的NTCTZNN模型比传统的CTZNN具有更强的抗噪能力。除此之外，为了实现潜在的数字硬件，在欧拉正向差分的基础上提出了离散时间版本的NTCTZNN模型（NTDTZNN）。最后，通过数值算例说明了所提出的NTCTZNN和NTDTZNN模型的有效性和准确性。