General 7-Instant DCZNN Model Solving Future Different-Level System of Nonlinear Inequality and Linear Equation

In this article, a novel and challenging problem called future different-level system of nonlinear inequality and linear equation (FDLSNILE) is proposed and investigated. To solve FDLSNILE, the corresponding continuous different-level system of nonlinear inequality and linear equation (CDLSNILE) is first analyzed, and then, a continuous combined zeroing neural network (CCZNN) model for solving CDLSNILE is proposed. To obtain a discrete combined zeroing neural network (DCZNN) model for solving FDLSNILE, a high-precision general 7-instant Zhang et al. discretization (ZeaD) formula for the first-order time derivative approximation is proposed. Furthermore, by applying the general 7-instant ZeaD formula to discretize the CCZNN model, a general 7-instant DCZNN (7IDCZNN) model is thus proposed for solving FDLSNILE. For comparison, by using three conventional ZeaD formulas, three conventional DCZNN models are also developed. Meanwhile, theoretical analyses and results guarantee the efficacy and superiority of the general 7IDCZNN model compared with the other three conventional DCZNN models for solving FDLSNILE. Finally, several comparative numerical experiments, including the motion control of a 5-link redundant manipulator, are provided to substantiate the efficacy and superiority of the general 7-instant ZeaD formula and the corresponding 7IDCZNN model.