Finite-Time and Predefined-Time Convergence Design for Zeroing Neural Network: Theorem, Method, and Verification

This article is primarily concerned with finite-time convergence (FTC) and predefined-time convergence (PTC) design for a class of general zeroing neural network (ZNN) by constructing different activation functions (AFs). Based on the limit comparison test for improper integrals, some useful theoretical criteria are proposed to determine whether a nonlinear-activated ZNN model has FTC, PTC, or not. This novel method can avoid the valuation loss of the zoom method and the unsolvable barrier of the direct integration method that are widely used in the previous ZNN design. According to these convergence criteria, some instructive corollaries are derived to design valuable AFs to make ZNN models with FTC or PTC more easily. By taking a matrix-inversion ZNN model, some commonly used AFs are used to verify the usability of the criteria. In addition, some new AFs are constructed to further design some better ZNN models with superior FTC or PTC. Finally, convergence types of the ZNN model based on different AFs are visualized in numerical experiments.