Exponential convergence of a learning controller for robot manipulators

The proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators is given. The learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly. Using the concepts of functional persistence of excitation and functional uniform complete observability, it is shown that, when a training task is selected for the robot which is persistently exciting, the learning controllers are globally exponentially stable. Repetitive controllers are always exponentially stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>