Frobenius Norm-Based Robust Dynamic Neural Network for Time-Dependent Matrix Inversion.

Abstract

Time-dependent matrix inversion (TDMI) is popularly utilized in scientific fields. Considering the low computing costs and simplified structure, this brief puts forward a Frobenius norm-based dynamic neural network (FNBDNN) model to address a TDMI problem for the first time, which achieves convergence within finite time and ensures strong robustness without using integral operations and element-wise nonlinear activation functions. Moreover, precise theoretical analyses are provided to display the property of finite-time convergence of the FNBDNN model in dealing with the TDMI problem. Simulation experiments are further conducted to verify the validity and preponderance of the FNBDNN model. Finally, an application of the devised FNBDNN model to the precise motion control of a two-axis manipulator is introduced.