Non-convex activated zeroing neural network model for solving time-varying nonlinear minimization problems with finite-time convergence

Abstract

Zeroing neural network (ZNN) model is a powerful tool for solving time-varying nonlinear minimization problems. This study presents some limitations of existing ZNN models, mainly related to convex and unsaturation constraints. To this end, a projection method is introduced for constructing non-convex activation functions, whereby a finite-time convergent non-convex zeroing neural network (FT-NCZNN) model is proposed based on this method. The model has a faster convergence rate than the original zeroing neural network (OZNN) model. Rigorous theoretical analyses are provided to verify the convergence of the model as well as the upper boundary on convergence time. Subsequently, through a series of simulations, the superior performance of the FT-NCZNN model under different noise conditions is demonstrated. Finally, an engineering application on motion generation is introduced for a double-linked manipulator to further illustrate the validity and feasibility of the FT-NCZNN model.