Robustness Analysis of a Fixed-Time Convergent GNN for Online Solving Sylvester Equation and Its Application to Robot Path Tracking

Abstract

It is shown in a recently published work that the GNN (gradient-based neural network) model activated by the msbp (modified sign-bi-power) function exhibits superior fixed-time convergence for solving the Sylvester equation in the noise-free case. Encouraged by this point, in this paper, we study its robust performance when it is disturbed by three kinds of noises, i.e., dynamic bounded vanishing noise, dynamic bounded non-vanishing noise, and constant noise. Detailed mathematical analyses are conducted to show the robustness properties (e.g., convergence property, the upper bound of steady-state solution error) of the GNN model, which are further verified by two simulation examples. Ultimately, the GNN model is applied to the path tracking of a planar four-link redundant robot arm.

Keywords

• Gradient-based neural network
• Sylvester equation
• robustness analysis
• robot path tracking