A novel finite-time convergent zeroing neural network (ZNN) based on varying gain parameter for solving time-varying (TV) problems is presented. The model is based on the improvement and generalization of the finite-time ZNN (FTZNN) dynamics by means of the varying-parameter ZNN (VPZNN) dynamics, and termed as VPFTZNN. More precisely, the proposed model replaces fixed and large values of the scaling parameter by an appropriate time-dependent gain parameter, which leads to a faster and bounded convergence of the error function in comparison to previous ZNN methods. The convergence properties of the proposed VPFTZNN dynamical evolution in its generic form is verified. Particularly, VPFTZNN for solving linear matrix equations and for computing generalized inverses are investigated theoretically and numerically. Moreover, the proposed design is applicable in solving the TV matrix inversion problem, solving the Lyapunov and Sylvester equation as well as in approximating the matrix square root. Theoretical analysis as well as simulation results validate the effectiveness of the introduced dynamical evolution. The main advantages of the proposed VPFTZNN dynamics are their generality and faster finite-time convergence with respect to FTZNN models.

提出了一种基于可变增益参数的时变收敛归零神经网络（TVNN），用于解决时变（TV）问题。该模型基于可变参数ZNN（VPZNN）动力学对有限时间ZNN（FTZNN）动力学的改进和概括，称为VPFTZNN。更准确地说，所提出的模型用适当的时间相关增益参数代替了比例缩放参数的固定值和较大值，与以前的ZNN方法相比，这导致了误差函数的更快且有界收敛。验证了所提出的VPFTZNN动态演化的通用形式的收敛性。特别地，从理论上和数值上研究了用于求解线性矩阵方程和用于计算广义逆的VPFTZNN。此外，所提出的设计适用于解决电视矩阵反演问题，求解Lyapunov和Sylvester方程以及近似矩阵的平方根。理论分析和仿真结果验证了引入的动态演化的有效性。相对于FTZNN模型，所提出的VPFTZNN动力学的主要优点是它们的通用性和更快的有限时间收敛性。