During the process of the general practical applications and scientific researches, time varying issues are an inescapable challenge to be tackled. In this article, a pre-defined finite-time zeroing neural networks (PDFT-ZNN) is devoted to solve the linear time-variant matrix equation (TVME) within a finite time (FT), which contrasts with the general ZNN (G-ZNN) models with relatively long global convergence time. Moreover, the proposed PDFT-ZNN model’s convergence time could be calculated in advance by adhering to the designed system parameters; this has nothing to do with the model’s initial state. Additionally, after the convergence analysis, if the solution error is relative small, the simple and effective method is to introduce a linear item to accelerate the convergence speed, in comparison with only the power-type ZNN models. Theory-based analysis and simulation-based results further validate that, the neural state solved by the presented FT-ZNN model can reach the theory-based solution of within the pre-defined finite time.

中文翻译：

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时变矩阵方程的预定义有限时间神经求解器[公式省略]

在一般的实际应用和科学研究过程中，时变问题是一个不可避免的挑战。在本文中，预定义的有限时间归零神经网络（PDFT-ZNN）致力于在有限时间（FT）内求解线性时变矩阵方程（TVME），这与一般的ZNN（G- ZNN）具有相对较长的全局收敛时间的模型。此外，所提出的PDFT-ZNN模型的收敛时间可以通过遵循设计的系统参数来提前计算；这与模型的初始状态无关。另外，在收敛分析后，如果求解误差较小，与仅采用幂型ZNN模型相比，简单有效的方法是引入线性项来加快收敛速度​​。基于理论的分析和基于仿真的结果进一步验证了所提出的FT-ZNN模型求解的神经状态可以在预定的有限时间内达到基于理论的解。