Two DTZNN Models of O(τ⁴) Pattern for Online Solving Dynamic System of Linear Equations: Application to Manipulator Motion Generation

Abstract

In this paper, firstly, a high accuracy one-step-ahead numerical differentiation formula with O(τ 4) pattern is proposed for discretization. Meanwhile, a high precision first-order derivative formula of the backward difference rule with O(τ 4) pattern error is given to approximate the derivative information. Then, two high accuracy discrete-time zeroing-type models (HADTZTM) with O(τ 4) pattern, i.e., HADTZTM with derivative information known (HADTZTM-K) and HADTZTM with derivative information unknown (HADTZTM-U), are developed, analyzed and investigated for online solving the dynamic system of linear equations (DSLEs). In addition, the 0-stability, consistency, and convergence of the HADTZTM-K and HADTZTM-U are verified for DSLEs. From a theoretical/numerical viewpoint, the classical models are revisited and analyzed for online solving DSLEs. Ultimately, simulation experiment including an application to the path-tracking of the four-link planar manipulator is conducted to demonstrate the efficiency and superiority of the HADTZTM-K and HADTZTM-U, where the HADTZTM-U overcomes the difficulty of derivative information unknown in practical applications. INDEX TERMS Dynamic system of linear equations (DSLEs), discrete-time zeroing neural network (DTZNN), backward difference formula, theoretical results, steady-state residual error.

Applications of Zeroing Neural Networks: A Survey

“…2020) aimed to enhance the accuracy of manipulator path tracking. They introduced a high accuracy first-order derivative approximation formula for discretization, and subsequently developed two models: HADTZTM-K (high accuracy discrete-time zeroing-type model with known derivative information) and HADTZTM-U (high accuracy discrete-time zeroing-type model with unknown derivative information) [71]. These models were applied to the pathtracking of a four-link planar manipulator, yielding favorable outcomes.…”

A neural network-based model for lower limb continuous estimation against the disturbance of uncertainty

“…In [25], the ZNN model is comprehensively interpreted, with the core idea being the construction of an error function. Besides, a noise-tolerant zeroing neural network model is proposed considering the nonlinear system with various noises [28][29][30][31]. [31] surmounts the disadvantage that traditional solvers can only handle static problems.…”

“…Besides, a noise-tolerant zeroing neural network model is proposed considering the nonlinear system with various noises [28][29][30][31]. [31] surmounts the disadvantage that traditional solvers can only handle static problems. The effectiveness and advancement of the two discrete-time ZNN models proposed from both theoretical and numerical perspectives are proved by taking a planar four-link manipulator as an example.…”

LS-SVM Combined with ZNN for Predicting the Continuous Motion Joint Angle of Lower Limb

“…In this paper, a method based on least squares support vector machine (LS-SVM) [22] combined with zeroing neural network (ZNN) [23][24][25] is proposed to predict the lower limb knee joint angle. LS-SVM is an improved algorithm of SVM.…”