Controllability distributions and systems approximations: a geometric approach

A.C. Ruiz, Henk Nijmeijer

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    27 Downloads (Pure)

    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 languageUndefined
    Title of host publication31st IEEE Conference on Decision and Control
    Place of PublicationTucson, Arizona
    PublisherIEEE
    Pages90-95
    Number of pages0
    Publication statusPublished - 16 Dec 1992
    Event31st IEEE Conference on Decision and Control, CDC 1992 - Westin La Paloma, Tucson, United States
    Duration: 16 Dec 199218 Dec 1992
    Conference number: 31

    Publication series

    Name
    PublisherIEEE
    Volume1

    Conference

    Conference31st IEEE Conference on Decision and Control, CDC 1992
    Abbreviated titleCDC
    CountryUnited States
    CityTucson
    Period16/12/9218/12/92

    Keywords

    • METIS-141523
    • IR-30882

    Cite this

    Ruiz, A. C., & Nijmeijer, H. (1992). Controllability distributions and systems approximations: a geometric approach. In 31st IEEE Conference on Decision and Control (pp. 90-95). Tucson, Arizona: IEEE.
    Ruiz, A.C. ; Nijmeijer, Henk. / Controllability distributions and systems approximations: a geometric approach. 31st IEEE Conference on Decision and Control. Tucson, Arizona : IEEE, 1992. pp. 90-95
    @inproceedings{48f624e64717443f841a1d2c355c711f,
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    year = "1992",
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    Ruiz, AC & Nijmeijer, H 1992, Controllability distributions and systems approximations: a geometric approach. in 31st IEEE Conference on Decision and Control. IEEE, Tucson, Arizona, pp. 90-95, 31st IEEE Conference on Decision and Control, CDC 1992, Tucson, United States, 16/12/92.

    Controllability distributions and systems approximations: a geometric approach. / Ruiz, A.C.; Nijmeijer, Henk.

    31st IEEE Conference on Decision and Control. Tucson, Arizona : IEEE, 1992. p. 90-95.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

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    AU - Nijmeijer, Henk

    PY - 1992/12/16

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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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    KW - IR-30882

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    Ruiz AC, Nijmeijer H. Controllability distributions and systems approximations: a geometric approach. In 31st IEEE Conference on Decision and Control. Tucson, Arizona: IEEE. 1992. p. 90-95