Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Discrete Control Systems

  • Taeyoung Lee
  • Melvin Leok
  • Harris McClamroch
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_126

Definition of the Subject

Discrete control systems, as considered here, refer to the control theory of discrete‐time Lagrangian or Hamiltonian systems. Thesediscrete‐time models are based on a discrete variational principle , andare part of the broader field of geometric integration . Geometric integrators are numericalintegration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They alsoguarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-bodydynamics.

In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability,controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of thecorresponding control problems. Despite the critical role of geometry and mechanics in...

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Notes

Acknowledgments

TL and ML have been supported in part by NSF Grant DMS‐0504747 and DMS-0726263. TL and NHM have been supported in part by NSF GrantECS-0244977 and CMS-0555797.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Taeyoung Lee
    • 1
  • Melvin Leok
    • 2
  • Harris McClamroch
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA