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(τ4) pattern is proposed for discretization. Meanwhile, a high precision first-order derivative formula of the backward difference rule with O(τ4) pattern error is given to approximate the derivative information. Then, two high accuracy discrete-time zeroing-type models (HADTZTM) with O(τ4) 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.

Keywords

• Dynamic system of linear equations (DSLEs)
• discrete-time zeroing neural network (DTZNN)
• backward difference formula
• theoretical results
• steady-state residual error