Barrier Function-Based Adaptive Lyapunov Redesign for Systems Without <i>A Priori</i> Bounded Perturbations
Christopher D. Cruz‐Ancona, Manuel A. Estrada, Leonid Fridman
Abstract
The problem of an adaptive Lyapunov redesign is revisited for a class of systems without <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the function majoring nonlinear uncertainties and disturbances. An adaptive barrier function-based gain for unit control is proposed, ensuring an arbitrary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> predefined uniform ultimate bound for solutions despite the presence of uncertainties and disturbances. The usage of positive semi-definite barrier function generates a continuous control signal adjusting the chattering, when the perturbations are decreasing to zero.