Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems
The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a...
Saved in:
| Main Author: | |
|---|---|
| Format: | article |
| Language: | EN |
| Published: |
MDPI AG
2021
|
| Subjects: | |
| Online Access: | https://doaj.org/article/69378a0b84d541b89fe55b643512259f |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper. |
|---|