Controllability of Some Nonlinear Systems with Drift via Generalized Curvature Properties

We discuss the problem of local attainability for finite-dimensional nonlinear control systems with quite general assumptions on the target set. Special emphasis is given to control-affine systems with a possibly nontrivial drift term. To this end, we provide some sufficient conditions ensuring loca...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on control and optimization 2015-01, Vol.53 (1), p.434-474
Main Authors: Marigonda, Antonio, Rigo, Silvia
Format: Article
Language:English
Subjects:
Control systems
Controllability
Curvature
Drift
Dynamical systems
Lie groups
Mathematical analysis
Optimization
Representations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss the problem of local attainability for finite-dimensional nonlinear control systems with quite general assumptions on the target set. Special emphasis is given to control-affine systems with a possibly nontrivial drift term. To this end, we provide some sufficient conditions ensuring local attainability, which involve geometric properties both of the target itself (such as a notion of generalized curvature), and of the Lie algebra associated with the control system. The main technique used is a convenient representation formula for the power expansion of the distance function along the trajectories, made at points sufficiently near to the target set.
ISSN:0363-0129
1095-7138
DOI:10.1137/130920691