Xiao Lin, He Yongjun, Wang Yaonan, Dai Jianhua, Wang Ran, Tang Wensheng
IEEE Trans Neural Netw Learn Syst. 2023 May;34(5):2413-2424. doi: 10.1109/TNNLS.2021.3106640. Epub 2023 May 2.
As a category of the recurrent neural network (RNN), zeroing neural network (ZNN) can effectively handle time-variant optimization issues. Compared with the fixed-parameter ZNN that needs to be adjusted frequently to achieve good performance, the conventional variable-parameter ZNN (VPZNN) does not require frequent adjustment, but its variable parameter will tend to infinity as time grows. Besides, the existing noise-tolerant ZNN model is not good enough to deal with time-varying noise. Therefore, a new-type segmented VPZNN (SVPZNN) for handling the dynamic quadratic minimization issue (DQMI) is presented in this work. Unlike the previous ZNNs, the SVPZNN includes an integral term and a nonlinear activation function, in addition to two specially constructed time-varying piecewise parameters. This structure keeps the time-varying parameters stable and makes the model have strong noise tolerance capability. Besides, theoretical analysis on SVPZNN is proposed to determine the upper bound of convergence time in the absence or presence of noise interference. Numerical simulations verify that SVPZNN has shorter convergence time and better robustness than existing ZNN models when handling DQMI.
作为递归神经网络（RNN）的一个类别，归零神经网络（ZNN）能够有效处理时变优化问题。与需要频繁调整以实现良好性能的固定参数ZNN相比，传统的可变参数ZNN（VPZNN）不需要频繁调整，但其可变参数会随着时间增长趋于无穷大。此外，现有的抗噪ZNN模型在处理时变噪声方面表现不佳。因此，本文提出了一种用于处理动态二次最小化问题（DQMI）的新型分段VPZNN（SVPZNN）。与之前的ZNN不同，SVPZNN除了两个特殊构造的时变分段参数外，还包括一个积分项和一个非线性激活函数。这种结构保持了时变参数的稳定，使模型具有很强的抗噪能力。此外，还对SVPZNN进行了理论分析，以确定在无噪声干扰或有噪声干扰情况下收敛时间的上限。数值模拟验证了SVPZNN在处理DQMI时比现有ZNN模型具有更短的收敛时间和更好的鲁棒性。
