Local asymptotic approximation of non-linear control systems!

Alberto Bressan

doi:10.1080/0020718508961201

Local asymptotic approximation of non-linear control systems!

Alberto Bressan

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

20 Scopus citations

Abstract

Let g₁, …, g_m be smooth vector fields on R^d. Using a canonical linear rescaling of time and space coordinates, the control system is transformed into a system, on the same state space, which is arbitrarily close to a nilpotent one. This approximation takes place in the C^∞ topology, and is particularly useful for the study of local properties of (+) which depend on the high-order variational structure of the vector fields g_i.

Original language	English (US)
Pages (from-to)	1331-1336
Number of pages	6
Journal	International Journal of Control
Volume	41
Issue number	5
DOIs	https://doi.org/10.1080/0020718508961201
State	Published - May 1985

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications

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10.1080/0020718508961201

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title = "Local asymptotic approximation of non-linear control systems!",

abstract = "Let g1, …, gm be smooth vector fields on Rd. Using a canonical linear rescaling of time and space coordinates, the control system is transformed into a system, on the same state space, which is arbitrarily close to a nilpotent one. This approximation takes place in the C∞ topology, and is particularly useful for the study of local properties of (+) which depend on the high-order variational structure of the vector fields gi.",

author = "Alberto Bressan",

note = "Funding Information: Received 31 August 1984. t Supported by the U.S. Army under Contract DAAG29-80-C-0041. t Istituto di Matematica Applicata, Universita di Padova, 35131 Padova, Via Belzoni 7, Italy.",

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N1 - Funding Information: Received 31 August 1984. t Supported by the U.S. Army under Contract DAAG29-80-C-0041. t Istituto di Matematica Applicata, Universita di Padova, 35131 Padova, Via Belzoni 7, Italy.

PY - 1985/5

Y1 - 1985/5

N2 - Let g1, …, gm be smooth vector fields on Rd. Using a canonical linear rescaling of time and space coordinates, the control system is transformed into a system, on the same state space, which is arbitrarily close to a nilpotent one. This approximation takes place in the C∞ topology, and is particularly useful for the study of local properties of (+) which depend on the high-order variational structure of the vector fields gi.

AB - Let g1, …, gm be smooth vector fields on Rd. Using a canonical linear rescaling of time and space coordinates, the control system is transformed into a system, on the same state space, which is arbitrarily close to a nilpotent one. This approximation takes place in the C∞ topology, and is particularly useful for the study of local properties of (+) which depend on the high-order variational structure of the vector fields gi.

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DO - 10.1080/0020718508961201

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JO - International Journal of Control

JF - International Journal of Control

IS - 5

ER -

Local asymptotic approximation of non-linear control systems!

Abstract

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