A remark on nonlinear accessibility conditions and infinite prolongations

Michel Fliess; Jean Lévine; Philippe Martin; François Ollivier; Pierre Rouchon

doi:10.1016/S0167-6911(97)00028-5

A remark on nonlinear accessibility conditions and infinite prolongations

Michel Fliess
, Jean Lévine
, Philippe Martin
, François Ollivier
, Pierre Rouchon

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

Abstract

The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without distinguishing between the system variables and is independent of time-scalings. Weak accessibility is also considered.

Original language	English
Pages (from-to)	77-83
Number of pages	7
Journal	Systems and Control Letters
Volume	31
Issue number	2
DOIs	https://doi.org/10.1016/S0167-6911(97)00028-5
Publication status	Published - 1 Jan 1997

Keywords

Diffieties
First integrals
Flatness
Jets
Lie brackets
Nonlinear controllability
Prolongations
Strong accessibility
Weak accessibility

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10.1016/S0167-6911(97)00028-5

Cite this

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title = "A remark on nonlinear accessibility conditions and infinite prolongations",

abstract = "The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without distinguishing between the system variables and is independent of time-scalings. Weak accessibility is also considered.",

keywords = "Diffieties, First integrals, Flatness, Jets, Lie brackets, Nonlinear controllability, Prolongations, Strong accessibility, Weak accessibility",

author = "Michel Fliess and Jean L{\'e}vine and Philippe Martin and Fran{\c c}ois Ollivier and Pierre Rouchon",

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AU - Fliess, Michel

AU - Lévine, Jean

AU - Martin, Philippe

AU - Ollivier, François

AU - Rouchon, Pierre

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without distinguishing between the system variables and is independent of time-scalings. Weak accessibility is also considered.

AB - The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without distinguishing between the system variables and is independent of time-scalings. Weak accessibility is also considered.

KW - Diffieties

KW - First integrals

KW - Flatness

KW - Jets

KW - Lie brackets

KW - Nonlinear controllability

KW - Prolongations

KW - Strong accessibility

KW - Weak accessibility

U2 - 10.1016/S0167-6911(97)00028-5

DO - 10.1016/S0167-6911(97)00028-5

M3 - Article

AN - SCOPUS:0031186755

SN - 0167-6911

VL - 31

SP - 77

EP - 83

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 2

ER -

A remark on nonlinear accessibility conditions and infinite prolongations

Abstract

Keywords

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