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 JACO $^2$ 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. [ABSTRACT FROM AUTHOR]