Norm-based zeroing neural dynamics for time-variant non-linear equations

Abstract

Zeroing neural dynamic (ZND) model is widely deployed for time-variant non-linear equations (TVNE). Various element-wise non-linear activation functions and integration operations are investigated to enhance the convergence performance and robustness in most proposed ZND models for solving TVNE, leading to a huge cost of hardware implementation and model complexity. To overcome these problems, the authors develop a new norm-based ZND (NBZND) model with strong robustness for solving TVNE, not applying element-wise non-linear activated functions but introducing a two-norm operation to achieve finite-time convergence. Moreover, the authors develop a discrete-time NBZND model for the potential deployment of the model on digital computers. Rigorous theoretical analysis for the NBZND is provided. Simulation results substantiate the advantages of the NBZND model for solving TVNE.