Some Applications of Differential Geometry in Control
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.
KeywordsGeometric Object Method Input State Manifold Pfaffian System Abstract Differential Geometry
Unable to display preview. Download preview PDF.
- 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