Controlled Lagrangians and potential shaping for stabilization of discrete mechanical systems

Anthony Bloch, Melvin Leok, Jerrold Marsden, and Dmitry Zenkov

Proc. 45th IEEE Conf. on Decision and Control, (2006), 3333-3338

Abstract:

The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary for matching in the discrete context are introduced. The theory is illustrated with the problem of stabilization of the cartpendulum system on an incline. We also discuss digital and model predictive control.