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.
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