Dual Performance Zeroing Neural Dynamics for Calculating Time-varying Linear Matrix Equations

An excellent activation function (AF) can improve the convergence speed and robustness of the Recurrent neural dynamic (RND) model. However, the existing AF can only improve the convergence speed, and the implementation of robustness needs to improve the unified formula. It is very rare that AF can achieve both prescribed time convergence and strong robustness. Therefore, in order to achieve both prescribed time convergence and strong robustness, two new nonlinear activation functions (AFs) are designed and embedded in the RND model to calculate time-varying linear matrix equations (LMEs) in different noise environments. In the theoretical analysis, we use Lyapunov theory to prove the stability, convergence and noise tolerance of RND model. In addition, in the numerical experiments, the existing four AFs are compared to verify that the RND model with the two nonlinear AFs has faster convergence rate and stronger noise tolerance in the calculation of time-varying LMEs.