Small-Time Stabilization of Homogeneous Cascaded Systems with Application to the Unicycle and the Slider Examples

Brigitte d'Andréa-Novel , Jean-Michel Coron , Wilfrid Perruquetti (1, 2)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Centrale Lille

This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of time-invariant continuous state feedback laws. This is the case of nonholonomic systems, an example being the "unicycle-like" mobile robot, or for underactuated mechanical systems, an example being the slider. Explicit time-varying feedback laws leading to small-time stabilization are constructed for these two control systems. The main tools are homogeneity, backstepping, and desingularization technics.

Mots clés: Nonholonomic kinematic; underactuated mechanical systems; small-time stabiliza- tion; homogeneity; time-varying feedback

Domaines: Automatique

Brigitte d'Andréa-Novel, Jean-Michel Coron, Wilfrid Perruquetti. Small-Time Stabilization of Homogeneous Cascaded Systems with Application to the Unicycle and the Slider Examples. SIAM Journal on Control and Optimization, 2020, 58 (5), pp.2997-3018. ⟨10.1137/19M1285081⟩. ⟨hal-02998430⟩