Future Different-Layer Linear Equation and Bounded Inequality Solved by Combining Adams–Bashforth Methods With CZNN Model

In this article, future different-layer linear equation and bounded inequality (DLLEBI) is investigated as a new and challenging problem. The continuous bounded inequality is converted into equality by introducing a time-variant nonnegative vector. A continuous zeroing neural network (CZNN) model is proposed for solving the corresponding continuous DLLEBI by utilizing the ZNN method. Adams-Bashforth (AB) methods are combined with the CZNN model to improve the computational precision. Hence, AB discrete ZNN (AB-DZNN) models are proposed to solve future DLLEBI. Specifically, a four-step AB-DZNN model with high precision is proposed. Three-, two-, and one-step AB-DZNN models are also developed for comparative analyses. Theoretical analyses and numerical results substantiate the validity and superiority of the proposed four-step AB-DZNN model for solving future DLLEBI. In addition, motion control problems of three-link, mobile, and physical Kinova JACO² robot arms are formulated as three specific future DLLEBI problems. These problems can be solved by the four proposed AB-DZNN models. Comparative numerical results provide further evidence that the proposed four-step AB-DZNN model has the most superior computational performance among the four AB-DZNN models.