Stability and regulation of nonsmooth dynamical systems

Abstract

The mathematical analysis of nonsmooth Lagrangian dynamical systems leads to introduce mathematical tools which are unusual in control theory, velocities with locally bounded variations, measure accelerations, measure differential inclusions to name a few. The control theory for such dynamical systems is just beginning to appear, and even the basic Lyapunov stability theory still needs to be stated. We will be able though to propose a Lagrange-Dirichlet theorem for nonsmooth Lagrangian dynamical systems that will be applied through Potential Shaping to the regulation of the position and force of a robotic manipulator.