Finite-Time <inline-formula> <tex-math notation="LaTeX">${H_\infty }$</tex-math> </inline-formula> Control for High-Precision Tracking in Robotic Manipulators Using Backstepping Control

Abstract

In this study, a finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller for uncertain robotic manipulators that achieves high-precision tracking performance without requiring the solution of a Hamilton-Jacobi equation or a Riccati equation is derived using the backstepping method. First, a theory of robust finite-time stability for a class of uncertain nonlinear systems is studied. This theory is then used to develop a simple robust tracking controller for robotic manipulators that provides high precision, strong robustness, and fast response. Not only is the closed-loop system globally finite-time stable, but the L2 gain is also less than or equal to γ. Simulations and experiments indicate that the proposed control approach is highly effective.