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

Abstract

The paper by Loria et al. is an expanded and refined version of Ref. (9). The central result is a proof of uniform global asymptotic stability (UGAS) for the feedback loop consisting of a dynamical plant mod- eled using Euler-Lagrange equations of motion (5,11) and of the adaptive controller of Slotine and Li pro- posed in Ref. (13). It is stated that the property of UGAS also holds when the same plant is controlled with several others passivity-based adaptive con- trollers. The UGAS of the considered closed-loop systems is established based on the property of uniform � -persistency of excitation (8), which is a relaxation of the persistency of excitation condition as formulated in Ref. (12). The relaxed property is also used to derive sufficient conditions for uniform local exponential stability of the plant controlled by a general adaptive control algorithm. As appealing result, the authors point out that the paper establishes a mathematical basis for analytical evaluation of robustness of the considered adaptive control algo- rithms against exogenous disturbances (e.g., mea- surement noise). By presenting experimental results of a robot motion control using the adaptive control algorithm of Slotine and Li, the authors want to empirically illustrate the robustness of this control algorithm. The robustness, as they claim, follows from the UGAS property proven by theoretical analysis. The theoretical results presented in the paper deserve credit, since they extend the mathematical