Advertisement

Some Applications of Differential Geometry in Control

  • Kurt Schlacher
  • Stefan Fuchshumer
  • Johann Holl
Part of the International Centre for Mechanical Sciences book series (CISM, volume 444)

Abstract

Differential geometry has been introduced to control about 25 years ago. This contribution shows, how one can identify dynamic systems with geometric objects defined on certain manifolds such that one obtains a coordinate free description of the systems. Based on this approach basic properties like accessibility and observability will be introduced. After that, tests, whether a system shows these properties, are presented. To show the power of the geometric approach for the control loop design, the two methods input to output and input to state linearization have been selected. Finally, it is worth mentioning that all the presented methods can easily be implemented in any advanced computer algebra system.

Keywords

Geometric Object Method Input State Manifold Pfaffian System Abstract Differential Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. A. Isidori. Nonlinear Control Systems. Springer, London, UK, 1995.CrossRefMATHGoogle Scholar
  2. H. Nijmeijer and A.J. van der Schaft. Nonlinear Dynamical Control Systems. Springer, New York, 1990.CrossRefMATHGoogle Scholar
  3. S. Sastry. Nonlinear Systems Analysis, Stability and Control. Springer, New York, 1999. D.J. Saunders. The Geometry of Jet Bundles. Cambridge University Press, Cambridge, UK, 1989.Google Scholar

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Kurt Schlacher
    • 1
  • Stefan Fuchshumer
    • 1
  • Johann Holl
    • 1
  1. 1.Institute of Automatic Control and Control Systems TechnologyJohannes Kepler University of LinzAustria

Personalised recommendations