Adaptive control of nonlinear system with time delay based on the feedback error learning method

Abstract

Aims to establish control theoretical validity of the feedback error learning (FEL) method for nonlinear manipulator dynamics including a time delay. It was shown in a practical two-links DD arm that with 200 milliseconds time delay in the feedback loop, the FEL method worked stably and tracking errors of the angles converged. In the paper, for the time delayed nonlinear systems, the stability of the adaptive control law of the FEL method is proven based on the small-gain theorem of nonlinear systems and Lyapunov stability theorem via a delayed state derivative.