Solving Future Different-Layer Nonlinear and Linear Equation System Using New Eight-Node DZNN Model

Abstract

In this article, a future different-layer nonlinear and linear equation system (DLNLES) is investigated. First, based on a zeroing neural network (ZNN) method, a zeroing equivalency theorem is proposed. Then, a continuous ZNN (CZNN) model is developed for continuous DLNLES solving. Next, a new eight-node Zhang et al. discretization formula is proposed to discretize the CZNN model, and thus, an eight-node discrete ZNN (DZNN) model is proposed for the future DLNLES solving. Five-node and four-node DZNN models are also developed for the same problem solving. Besides, numerical experiments are executed to substantiate the validity and superiority of the proposed eight-node DZNN model. Finally, the path-tracking control problem of a four-link redundant robot arm is formulated as a specific future DLNLES problem and can, thus, be solved by the three DZNN models. Comparative numerical results further indicate that the proposed eight-node DZNN model is much superior to the other two DZNN models.