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

This paper aims to establish control theoretical validity of the feedback error learning (FEL) method for nonlinear manipulator dynamics including a time delay. The FEL method is used for two degrees of freedom control system in order to construct an inverse model of a controlled object as the feedfoward controller adaptively. This framework was studied for the brain motor control of human being, the adaptive control of robot arm and other complicated nonlinear control systems. In practical two-links DD arm, it was shown that with 200 milliseconds time delay in the feedback loop, the FEL method worked stably and tracking errors of the angles converged. In this paper, for the time delayed nonlinear systems, the stability of the adaptive control law of FEL method is proven based on the small-gain theorem of nonlinear systems and Lyapunov stability theorem via a delayed state derivative.