End point trajectory control with internal stability of a flexible link by learning

In this paper we present a novel finite dimensional learning algorithm for end point trajectory control of a flexible link moving on a horizontal plane. Given a desired end point trajectory generated by a finite dimensional exosystem, by means of successive trials, the algorithm proposed learns the initial state and the control needed to exactly track the desired trajectory. An internal stability constraint is also enforced, which prevents undesirable excessive vibrations and control effort. Initialization of the flexible link state is automatically accomplished as a part of the same learning process. Algorithm ability of fully rejecting linear plant perturbations and disturbances which are linear functions of the exosystem state is formally proven. Experimental results show the effectiveness of the algorithm introduced and its robustness with respect to nonlinear plant perturbations and unmodeled dynamics