NECESSARY CONDITIONS FOR LOCAL CONTROLLABILITY OF A PARTICULAR CLASS OF SYSTEMS WITH TWO SCALAR CONTROLS

Laetitia Giraldi; Pierre Lissy; Clément Moreau; Jean Baptiste Pomet

doi:10.1051/cocv/2023073

NECESSARY CONDITIONS FOR LOCAL CONTROLLABILITY OF A PARTICULAR CLASS OF SYSTEMS WITH TWO SCALAR CONTROLS

Laetitia Giraldi
, Pierre Lissy
, Clément Moreau
, Jean Baptiste Pomet

Research output: Contribution to journal › Article › peer-review

Abstract

We consider control-affine systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L^∞ or small in W^1,∞. These results are illustrated with several examples.

Original language	English
Article number	4
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	30
DOIs	https://doi.org/10.1051/cocv/2023073
Publication status	Published - 1 Jan 2024
Externally published	Yes

Keywords

Controllability
control theory

Access to Document

10.1051/cocv/2023073

Cite this

@article{e3eac98c232746f4b1bcdd4d64d143eb,

title = "NECESSARY CONDITIONS FOR LOCAL CONTROLLABILITY OF A PARTICULAR CLASS OF SYSTEMS WITH TWO SCALAR CONTROLS",

abstract = "We consider control-affine systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L∞ or small in W1,∞. These results are illustrated with several examples.",

keywords = "Controllability, control theory",

author = "Laetitia Giraldi and Pierre Lissy and Cl{\'e}ment Moreau and Pomet, \{Jean Baptiste\}",

year = "2024",

month = jan,

day = "1",

doi = "10.1051/cocv/2023073",

language = "English",

volume = "30",

journal = "ESAIM - Control, Optimisation and Calculus of Variations",

issn = "1292-8119",

}

TY - JOUR

T1 - NECESSARY CONDITIONS FOR LOCAL CONTROLLABILITY OF A PARTICULAR CLASS OF SYSTEMS WITH TWO SCALAR CONTROLS

AU - Giraldi, Laetitia

AU - Lissy, Pierre

AU - Moreau, Clément

AU - Pomet, Jean Baptiste

PY - 2024/1/1

Y1 - 2024/1/1

N2 - We consider control-affine systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L∞ or small in W1,∞. These results are illustrated with several examples.

AB - We consider control-affine systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L∞ or small in W1,∞. These results are illustrated with several examples.

KW - Controllability

KW - control theory

UR - https://www.scopus.com/pages/publications/85183323637

U2 - 10.1051/cocv/2023073

DO - 10.1051/cocv/2023073

M3 - Article

AN - SCOPUS:85183323637

SN - 1292-8119

VL - 30

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 4

ER -

NECESSARY CONDITIONS FOR LOCAL CONTROLLABILITY OF A PARTICULAR CLASS OF SYSTEMS WITH TWO SCALAR CONTROLS

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this