Controllability distributions and systems approximations: a geometric approach

A.C. Ruiz; H. Nijmeijer

doi:10.1109/CDC.1992.371784

Controllability distributions and systems approximations: a geometric approach

A.C. Ruiz
, H. Nijmeijer

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the results

Original language	English
Title of host publication	31st IEEE Conference on Decision and Control (CDC 1992)
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	90-95
DOIs	https://doi.org/10.1109/CDC.1992.371784
Publication status	Published - 16 Dec 1992
Event	31st IEEE Conference on Decision and Control, CDC 1992 - Westin La Paloma, Tucson, United States Duration: 16 Dec 1992 → 18 Dec 1992 Conference number: 31

Conference

Conference	31st IEEE Conference on Decision and Control, CDC 1992
Abbreviated title	CDC
Country/Territory	United States
City	Tucson
Period	16/12/92 → 18/12/92

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10.1109/CDC.1992.371784

Ruiz1992controllabilityFinal published version, 683 KB

Controllability distributions and systems approximations: a geometric approach
Ruiz, A. C. & Nijmeijer, H., 1994, In: IEEE transactions on automatic control. 39, 7, p. 1473-1476 4 p.
Research output: Contribution to journal › Article › Academic › peer-review

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Controllability distributions and systems approximations: a geometric approach
Ruiz, A. C. & Nijmeijer, H., 1992, Enschede: University of Twente. 17 p. (Memorandum; no. 1040)
Research output: Book/Report › Report › Professional

Cite this

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title = "Controllability distributions and systems approximations: a geometric approach",

abstract = "Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the results",

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N2 - Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the results

AB - Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the results

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DO - 10.1109/CDC.1992.371784

M3 - Conference contribution

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EP - 95

BT - 31st IEEE Conference on Decision and Control (CDC 1992)

PB - IEEE

CY - Piscataway, NJ

Y2 - 16 December 1992 through 18 December 1992

ER -

Controllability distributions and systems approximations: a geometric approach

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