Title :
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems
Author :
Bloch, Anthony M. ; Leok, Melvin ; Marsden, Jerrold E. ; Zenkov, Dmitry V.
Author_Institution :
Dept. of Math., Michigan Univ., Ann Arbor, MI
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 cart-pendulum system on an incline. We also discuss digital and model predictive control
Keywords :
asymptotic stability; digital control; discrete systems; nonlinear control systems; predictive control; state-space methods; cart-pendulum system; controlled Lagrangians; controlled shape equation; digital control; discrete mechanical system; model predictive control; potential shaping; state-space asymptotic stabilization; Control systems; Digital control; Integral equations; Lagrangian functions; Mathematics; Mechanical systems; Predictive control; Predictive models; Shape control; USA Councils;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.376695
