Abstract
Although the feedback error learning (FEL) controller had been broadly applied to the robot manipulation problems, the complete proof of the asymptotic stability of the controlled system has not been given clearly. In the previous work, it was made clear that the asymptotically stable trajectory tracking can be achieved by introducing the saturated proportional feedback or third-order position error feedback into the feedback control loop in the FEL controller. However, in the practical robot manipulation, the simple linear PD feedback controller has been extensively used rather than such the nonlinear ones. Thus, this paper proposed a new FEL controller which consists of the linear PD feedback and the adaptive parameter estimation law composed of the off-line regressor matrix and saturated error signals. The asymptotic stability of the controlled system was proven along the LaSalle's invariance theorem for the non-autonomous system.
