Uniform parametric convergence in the adaptive control of manipulators: a case restudied

It is known in the practice of closed-loop identification of mechanical systems that, since the Langrangian dynamic model is linear in the constant physical parameters, a sufficient condition for parameter convergence is that the robot be made to follow reference trajectories which render the regressor matrix, persistently exciting. Slotine and Li established this many years ago for a particular adaptive controller. This result is based on adaptive linear systems theory and relies on the condition that the applied control law makes the robot asymptotically track the imposed rich reference trajectories. This paper revisits this problem and establishes a proof that this condition is not only sufficient but also necessary to establish the stronger property of uniform global asymptotic stability of the overall closed-loop system.