For solving dynamic generalized Lyapunov equation, two robust finite-time zeroing neural network (RFTZNN) models with stationary and nonstationary parameters are generated through the usage of an improved sign-bi-power (SBP) activation function (AF). Taking differential errors and model implementation errors into account, two corresponding perturbed RFTZNN models are derived to facilitate the analyses of robustness on the two RFTZNN models. Theoretical analysis gives the quantitatively estimated upper bounds for the convergence time (UBs-CT) of the two derived models, implying a superiority of the convergence that varying parameter RFTZNN (VP-RFTZNN) possesses over the fixed parameter RFTZNN (FP-RFTZNN). When the coefficient matrices and perturbation matrices are uniformly bounded, residual error of FP-RFTZNN is bounded, whereas that of VP-RFTZNN monotonically decreases at a super-exponential rate after a finite time, and eventually converges to 0. When these matrices are bounded but not uniform, residual error of FP-RFTZNN is no longer bounded, but that of VP-RFTZNN still converges. These superiorities of VP-RFTZNN are illustrated by abundant comparative experiments, and its application value is further proved by an application to robot.

中文翻译：

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用于求解动态广义李亚普诺夫方程的具有固定和变化参数的鲁棒有限时间归零神经网络


为了求解动态广义李亚普诺夫方程，通过使用改进的符号双幂（SBP）激活函数（AF）生成两个具有平稳和非平稳参数的鲁棒有限时间归零神经网络（RFTZNN）模型。考虑微分误差和模型实现误差，推导了两个相应的扰动RFTZNN模型，以便于分析这两个RFTZNN模型的鲁棒性。理论分析给出了两个推导模型的收敛时间（UBs-CT）的定量估计上限，这意味着变参数RFTZNN（VP-RFTZNN）比固定参数RFTZNN（FP-RFTZNN）具有收敛优势。当系数矩阵和扰动矩阵一致有界时，FP-RFTZNN的残差有界，而VP-RFTZNN的残差在有限时间后以超指数速率单调递减，最终收敛于0。当这些矩阵有界时但不均匀，FP-RFTZNN 的残差不再有界，但 VP-RFTZNN 的残差仍然收敛。通过大量的对比实验说明了VP-RFTZNN的这些优越性，并通过在机器人上的应用进一步证明了其应用价值。