Zeroing Neural Network for Solving Time-Varying Linear Equation and Inequality Systems

Abstract

A typical recurrent neural network called zeroing neural network (ZNN) was developed for time-varying problem-solving in a previous study. Many applications result in time-varying linear equation and inequality systems that should be solved in real time. This paper provides a ZNN model for determining the solution of time-varying linear equation and inequality systems. By introducing a nonnegative slack variable, the time-varying linear equation and inequality systems are transformed into a mixed nonlinear system. The ZNN model is established via the definition of an indefinite error function and the usage of an exponential decay formula. Theoretical results indicate the convergence property of the proposed ZNN model. Comparative simulation results prove the ZNN effectiveness and superiority for time-varying linear equation and inequality systems. Furthermore, the proposed ZNN model is employed to robot manipulators, thus showing the ZNN applicability.