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Published January 30, 2006 | Published
Book Section - Chapter Open

Controlled Lagrangians and Stabilization of the Discrete Cart-Pendulum System

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.

Additional Information

© 2005 IEEE. The authors would like to thank the reviewers for helpful remarks. The research of AMB was supported by NSF grants DMS-0103895, DMS-030583, and CMS-0408542. The research of ML was partially supported by NSF grant DMS- 0504747 and a University of Michigan Rackham faculty grant. The research of JEM was partially supported by ONR MURI Contract 00000916. The research of DVZ was partially supported by NSF grant DMS-0306017. AMB and DVZ would also like to thank the CRM, Barcelona, where part of this research was carried out.

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