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Stability Analysis of Trajectories on Manifolds with Applications to Observer and Controller Design

Wu, Dongjun LU ; Yi, Bowen and Rantzer, Anders LU orcid (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.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
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}},
}