Solving for Inverse-Like Dynamic Matrices of Variables and Derivatives Using Zhang Neural Dynamics (ZND) Equivalency

Abstract

Solving for inverse-like dynamic matrices of variables and derivatives is exciting and challenging. Although it may be encountered in the fields of industrial control or scientific research, it has not been widely studied because of its complexity and difficulty. In this work, to solve this problem, the Zhang neural dynamics (ZND, or called, zeroing neural dynamics) method is employed to the equivalent transformation of the original problem, and a model termed ZND equivalency (ZE) model is proposed and investigated. Meanwhile, a derivative dynamics (DD) model is proposed for comparison purposes. In order to facilitate the implementation of digital hardware, a five- instant Zhang et al discretization (ZeaD) formula is presented. Thus, two discrete models termed discrete-time ZE model and discrete-time DD model (in short DZE model and DDD model, respectively) are proposed by using the presented ZeaD formula. Theoretical analysis and numerical experimental results indicate the good performance, accuracy and superiority of the DZE model.