Finite-gain L<inf>2</inf> stability of anti-windup adaptive tracking control for Euler-Lagrange systems with actuator saturation

Abstract

The present paper describes finite-gain L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability guaranteed locally by the proposed anti-windup adaptive law for Euler-Lagrange systems with actuator saturation. All constant parameters of the robot system are estimated for an arbitrary target orbit. In order to achieve finite-gain L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability and ensure adaptive tracking performance, an output saturation function of the tracking error is introduced. The finite L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gains are derived considering four actuator saturation cases, and finite-gain L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability is guaranteed locally based on passivity. The control performance is verified through numerical simulations using a two-link robot arm.