Discontinuous feedback control of a special class of underactuated mechanical systems

We study a control problem for a special class of underactuated mechanical systems, namely for mechanical systems with several directly actuated degre es of freedom and a single unactuated degree of freedom that must be contro lled through the system coupling. Specific assumptions are introduced that define this class, which includes many important models of mechanical syste m examples. The main result of the paper is the construction of a discontin uous nonlinear feedback controller for which the closed loop equilibrium at the origin is made 'globally attractive'. The control construction approac h is introduced in detail, and a proof of attractiveness is presented. The results are applied to control of the planar motion of a rigid body with a single unactuated internal degree of freedom. Copyright (C) 2000 John Wiley & Sons, Ltd.