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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation
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Design and Analysis of Two Prescribed-Time and Robust ZNN Models With Application to Time-Variant Stein Matrix Equation

机译：用应用于时变斯坦矩阵方程的两个规定时间和鲁棒ZNN模型的设计与分析

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摘要

The zeroing neural network (ZNN) activated by nonlinear activation functions plays an important role in many fields. However, conventional ZNN can only realize finite-time convergence, which greatly limits the application of ZNN in a noisy environment. Generally, finite-time convergence depends on the original state of ZNN, but the original state is often unknown in advance. In addition, when meeting with different noises, the applied nonlinear activation functions cannot tolerate external disturbances. In this article, on the strength of this idea, two prescribed-time and robust ZNN (PTR-ZNN) models activated by two nonlinear activation functions are put forward to address the time-variant Stein matrix equation. The proposed two PTR-ZNN models own two remarkable advantages simultaneously: 1) prescribed-time convergence that does not rely on original states and 2) superior noise-tolerance performance that can tolerate time-variant bounded vanishing and nonvanishing noises. Furthermore, the detailed theoretical analysis is provided to guarantee the prescribed-time convergence and noise-tolerance performance, with the convergence upper bounds of steady-state residual errors calculated. Finally, simulative comparison results indicate the effectiveness and the superiority of the proposed two PTR-ZNN models for the time-variant Stein matrix equation solving.
机译：由非线性激活函数激活的归零神经网络（ZnN）在许多领域中起重要作用。然而，传统的ZnN只能实现有限时间的收敛，这极大地限制了ZnN在嘈杂环境中的应用。通常，有限时间收敛取决于ZnN的原始状态，但原始状态通常预先未知。另外，在满足不同的噪声时，所应用的非线性激活功能不能容忍外部干扰。在本文中，在该思想的强度上，提出了两个非线性激活功能激活的两个规定时间和鲁棒ZNN（PTR-ZNN）模型来解决时变斯坦矩阵方程。提出的两个PTR-ZNN模型同时拥有两个显着的优势：1）规定时间收敛，不依赖于原始状态，2）耐受时间变体有界消失和非垂体噪声的优越抗噪音性能。此外，提供了详细的理论分析，以保证规定时间收敛和噪声容差性能，并计算稳态残余误差的会聚上限。最后，模拟比较结果表明了所提出的两种PTR-ZNN模型的有效性和优越性，用于时变斯坦矩阵方程求解。

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