New Discrete-Solution Model for Solving Future Different-Level Linear Inequality and Equality With Robot Manipulator Control

Abstract

Different from general linear inequality or equality, the problem of future different-level linear inequality and equality (FDLLIE) is investigated, which is much more interesting and challenging. In order to solve this difficult FDLLIE, continuous different-level linear inequality and equality (CDLLIE) is first considered. A zeroing equivalency theorem is proposed based on the zeroing neural network method, and then a continuous solution model is, thus, obtained for CDLLIE solving. Furthermore, a new discrete-solution (NDS) model is developed for FDLLIE solving by using a proposed new 7-instant Zhang et al. discretization (ZeaD) formula to discretize the continuous solution model. Meanwhile, theoretical analyses and results are presented to show the excellent properties of the NDS model. Numerical results illustrate the effectiveness and superiority of the NDS model for solving FDLLIE. Furthermore, application experiments for motion planning of robot manipulator are conducted to substantiate the efficacy of the NDS model for FDLLIE solving.