On the use of configuration variables as control variables in mechanical systems

Abstract

The branch of control theory for Lagrangian mechanical systems where configuration variables are used as control variables is called here hyper-impulsive control theory. We suppose that part of system's coordinates are 'controllized', i.e. identified with a control function u that can be discontinuous. Due to the presence of the derivative of u in the dynamic equation, the resulting motion is discontinuous both in the configurations and momenta in the general case (hyper-impulsive motion). We briefly review the theory of hyper-impulsive motion, we study in detail the robustness of hyper-impulsive control and we apply the theory to test mechanical systems: the rigid body, a planar space robot and the ball in the hoop system.