Discussion on: "Uniform Parametric Convergence in the Adaptive Control of Mechanical Systems"

The paper under discussion [2] states that its main result is as follows. It considers several of the usual parameter adaptive control schemes for fully actuated mechanical systems and proves that persistency of excitation of the regressor matrix along the desired trajectory is a necessary and sufficient condition for uniform global asymptotic stability (UGAS) of the closed loop system. While the above result is a major contribution of the paper, it is a consequence of the more general result below on adaptively controlled systems which we consider to be the main result of the paper. Also, in presenting its results, reference [2] focuses mainly on the Slotine-Li adaptive controllers of [5, 6, 4]. However, it only considers special cases of the gain matrices originally considered by Slotine and Li. Here we demonstrate that the results of [2] also hold for the most general controllers considered in [5, 6, 4].