T-S Fuzzy Adaptive Control Based on Small Gain Approach for an Uncertain Robot Manipulators

In this paper, a T–S (Takagi–Sugeno) adaptive tracking algorithm control based on small gain theorem is proposed for an uncertain robot system with n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-link manipulators. A nonzero time-varying parameter is introduced in the common T–S fuzzy logic system, the T–S type fuzzy logic system with updated parameters laws is build, then the new and original universal approximation with parameter is introduced. The approximation accuracy can be updated on-line by the parameters, which is not limited by the number of fuzzy rules. With the novel property of universal approximation, the proposed adaptive control can be synthetized to overcome the limitations such as on-line learning computation burden in conventional fuzzy logic systems. The originality T–S fuzzy logic system is used to compensate the unknown model of robot manipulators and the adaptive tracking control algorithm is designed with the new property of universal approximation. Based on the analysis of small gain theorem and ISS theory (input-to-state stability), all signals in closed-loop system can be guaranteed to be bounded, and the system can be extended from semi-global stability to global stability by employing the proposed adaptive control scheme. Finally, simulation results are shown to demonstrate the effectiveness of the adaptive control scheme.