Finite-time stable versions of the continuous Newton method and applications to neural networks

Control theory has become a focus of research for evaluation and synthesis of numerical algorithms. In this paper, a finite-time version of the continuous Newton method is proposed using finite-time stability theory. Moreover, robustness of the proposed method under computational errors is discussed. It is also shown that the proposed approach can change the singularity structure of the Newton vector field. A finite-time continuous quasi Gauss-Newton’s method is also derived. The effectiveness as well as some limitations of the proposed methods in zero finding and optimization problems are illustrated via numerical examples