Abstract There are two equivalent methods for dealing with the nonlinearity of complex-valued problems. The first method is to handle the real part and imaginary part of complex inputs, and the second method is to handle the modulus of complex inputs. Based on these two methods, this paper explores a superior nonlinear activation function and proposes two improved finite-time zeroing neural network (IFTZNN) models for time-varying complex Sylvester equation solving. Regarding the existing neural model activated by the sign-bi-power (SBP) activation function, the convergence upper bounds of the IFTZNN models are much smaller, and thus we can estimate their convergence time more accurately. Furthermore, the detailed theoretical analysis of the IFTZNN models is provided to show their effectiveness. Comparative simulation results also verify the advantages of our proposed IFTZNN models for complex Sylvester equation solving.

中文翻译：

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用于时变复杂 Sylvester 方程求解的改进有限时间归零神经网络

摘要 有两种处理复值问题非线性的等效方法。第一种方法是处理复数输入的实部和虚部，第二种方法是处理复数输入的模数。基于这两种方法，本文探索了一种优越的非线性激活函数，并提出了两种改进的有限时间归零神经网络 (IFTZNN) 模型，用于时变复杂的 Sylvester 方程求解。对于由符号双幂（SBP）激活函数激活的现有神经模型，IFTZNN 模型的收敛上限要小得多，因此我们可以更准确地估计它们的收敛时间。此外，还提供了 IFTZNN 模型的详细理论分析以展示其有效性。