On the Finite-Time Regulation of Euler–Lagrange Systems Without Velocity Measurements

Motivated by the energy-shaping framework and the properties of homogeneous systems, in this paper, we solve the global regulation problem, in finite-time (FT), of a class of fully actuated Euler-Lagrange (EL) systems without requiring velocity measurements. As in the energy shaping methodology, the controller is another EL-system and the plant-controller interconnection is the gradient of a suitable defined potential function. The desired equilibrium point becomes globally asymptotically stable when 1) the desired equilibrium is unique and isolated; and 2) damping can be back-propagated from the controller to the plant. The potential energy and dissipation functions of the controller are designed to satisfy such requirements and to provide a closed-loop system that admits a homogeneous approximation of negative degree in order to ensure FT convergence. The proposed methodology allows to obtain different novel controllers.