Practical Stabilization of Driftless Systems on Lie Groups

Pascal Morin (1) , Claude Samson

1 ICARE - Instrumentation, control and architecture of advanced robots

A general control design approach for the stabilization of controllable driftless nonlinear systems on finite dimensional Lie groups is presented. The approach is based on the concept of transverse functions, the existence of which is equivalent to the system's controllability. Its outcome is the practical stabilization of any trajectory -i.e. not necessarily a solution of the control system--- in the state space. The possibility of applying the approach to an arbitrary controllable smooth driftless system follows in turn from the fact that any controllable homogeneous approximation of this system can be lifted (via a dynamic extension) to a system on a Lie group. Illustrative examples are given.

Mots clés: PRACTICAL STABILIZATION; NONLINEAR SYSTEM; LIE GROUP; HOMOGENEOUS VECTOR FIELD

Domaines: Autre [cs.OH]

Pascal Morin, Claude Samson. Practical Stabilization of Driftless Systems on Lie Groups. RR-4294, INRIA. 2001. ⟨inria-00072293⟩