Unified Model Solving Nine Types of Time-Varying Problems in the Frame of Zeroing Neural Network

Many time-varying problems have been solved using the zeroing neural network proposed by Zhang et al. In this article, nine types of time-varying problems, namely time-varying nonlinear equation system, time-varying linear equation system, time-varying convex nonlinear optimization under linear equalities, unconstrained time-varying convex nonlinear optimization, time-varying convex quadratic programming under linear equalities, unconstrained time-varying convex quadratic programming, time-varying nonlinear inequality system, time-varying linear inequality system, and time-varying division, are investigated to better understand the essence of zeroing neutral network. Discrete-form time-varying problems are studied by considering the nature of unknown future and the requirement of real-time computation for time-varying problems. A unified model is proposed in the frame of zeroing neural network to uniformly solve these time-varying problems on the basis of their connections and a newly developed discretization formula. Theoretical analyses and numerical experiments, including the tracking control of PUMA560 robot manipulator, verify the effectiveness and precision of the proposed unified model.

Automated summary

This article investigates nine types of time-varying problems using the zeroing neural network, proposing a unified model to solve these problems based on their connections and a newly developed discretization formula.