Stability Analysis of Trajectories on Manifolds with Applications to Observer and Controller Design
(2024) In IEEE Transactions on Automatic Control p.1-8- Abstract
This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the complete lift of the system along the given trajectory. These conditions are coordinate-free which reveal fundamental relationships between exponential stability and incremental stability in a local sense. We then apply these results to design tracking controllers and observers for Euler-Lagrangian systems on manifolds; a notable advantage of our design is that it visibly reveals the effect of curvature on system dynamics and hence suggests compensation terms in the controller and observer. Additionally, we... (More)
This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the complete lift of the system along the given trajectory. These conditions are coordinate-free which reveal fundamental relationships between exponential stability and incremental stability in a local sense. We then apply these results to design tracking controllers and observers for Euler-Lagrangian systems on manifolds; a notable advantage of our design is that it visibly reveals the effect of curvature on system dynamics and hence suggests compensation terms in the controller and observer. Additionally, we revisit some well-known intrinsic observer problems using our proposed method, which largely simplifies the analysis compared to existing results.
(Less)
- author
- Wu, Dongjun LU ; Yi, Bowen and Rantzer, Anders LU
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- epub
- subject
- keywords
- Control theory, Manifolds, Measurement, Observers, Stability analysis, Task analysis, Trajectory
- in
- IEEE Transactions on Automatic Control
- pages
- 8 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85192149685
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2024.3395023
- language
- English
- LU publication?
- yes
- id
- 0c74d509-1b82-48a6-9c38-d7fb228f63ff
- date added to LUP
- 2024-05-15 16:03:10
- date last changed
- 2024-05-15 16:03:49
@article{0c74d509-1b82-48a6-9c38-d7fb228f63ff, abstract = {{<p>This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the complete lift of the system along the given trajectory. These conditions are coordinate-free which reveal fundamental relationships between exponential stability and incremental stability in a local sense. We then apply these results to design tracking controllers and observers for Euler-Lagrangian systems on manifolds; a notable advantage of our design is that it visibly reveals the effect of curvature on system dynamics and hence suggests compensation terms in the controller and observer. Additionally, we revisit some well-known intrinsic observer problems using our proposed method, which largely simplifies the analysis compared to existing results.</p>}}, author = {{Wu, Dongjun and Yi, Bowen and Rantzer, Anders}}, issn = {{0018-9286}}, keywords = {{Control theory; Manifolds; Measurement; Observers; Stability analysis; Task analysis; Trajectory}}, language = {{eng}}, pages = {{1--8}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Automatic Control}}, title = {{Stability Analysis of Trajectories on Manifolds with Applications to Observer and Controller Design}}, url = {{http://dx.doi.org/10.1109/TAC.2024.3395023}}, doi = {{10.1109/TAC.2024.3395023}}, year = {{2024}}, }