Controlled Lagrangians and stabilization of the discrete cart-pendulum system

Bloch A. M., M. Leok, J. E. Marsden and D. Zenkov

Proc. CDC 44, 6579-6584

Abstract:

Matching techniques are developed for discrete mechanical systems with symmetry. We describe new phenomena that arise in the controlled Lagrangian approach for mechanical systems in the discrete context. In particular, one needs to either make an appropriate selection of momentum levels or introduce a new parameter into the controlled Lagrangian to complete the matching procedure. We also discuss digital and model predictive control.