# Design and analysis of combined discrete-time zeroing neural network for solving time-varying nonlinear equation with robot application

## TL;DR

This paper introduces a new combined discrete-time neural network model for solving time-varying nonlinear equations, with applications in robot motion planning.

## Contribution

A novel combined discrete-time zeroing neural network (CDTZNN) model is proposed to efficiently solve time-varying nonlinear equations.

## Key findings

- The CDTZNN model combines two discrete-time ZNN models to avoid direct Jacobian matrix inversion.
- Theoretical analysis and numerical experiments confirm the effectiveness of the proposed CDTZNN model.
- The model is successfully applied to robot manipulator motion planning, demonstrating its practical applicability.

## Abstract

Zeroing neural network (ZNN) is viewed as an effective solution to time-varying nonlinear equation (TVNE). In this paper, a further study is shown by proposing a novel combined discrete-time ZNN (CDTZNN) model for solving TVNE. Specifically, a new difference formula, which is called the Taylor difference formula, is constructed for first-order derivative approximation by following Taylor series expansion. The Taylor difference formula is then used to discretize the continuous-time ZNN model in the previous study. The corresponding DTZNN model is obtained, where the direct Jacobian matrix inversion is required (being time consuming). Another DTZNN model for computing the inverse of Jacobian matrix is established to solve the aforementioned limitation. The novel CDTZNN model for solving the TVNE is thus developed by combining the two models. Theoretical analysis and numerical results demonstrate the efficacy of the proposed CDTZNN model. The CDTZNN applicability is further indicated by applying the proposed model to the motion planning of robot manipulators.