In EDS ansehen

Minimal-time nonlinear control via semi-infinite programming

Gespeichert in:
Bibliographische Detailangaben
Titel: Minimal-time nonlinear control via semi-infinite programming
Autoren: Oustry, Antoine, Tacchi, Matteo
Weitere Verfasser: Optimization at LIX (OptimiX), Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX), École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), École nationale des ponts et chaussées (ENPC), GIPSA - Modelling and Optimal Decision for Uncertain Systems (GIPSA-MODUS), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA)
Quelle: https://hal.science/hal-04145402 ; 2025.
Verlagsinformationen: CCSD
Publikationsjahr: 2025
Bestand: Université Grenoble Alpes: HAL
Schlagwörter: Nonlinear control, Minimal time control, Weak formulation, Semi-infinite programming, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Beschreibung: We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values of which converge to the value of the control problem. These semi-infinite programs are increasing restrictions of the dual of the nonlinear control problem, which is a maximization problem over the subsolutions of the Hamilton-Jacobi-Bellman (HJB) equation. Our approach is compatible with generic dynamical systems and state constraints. Specifically, we use an oracle that, for a given differentiable function, returns a point at which the function violates the HJB inequality. We solve the semi-infinite programs using a classical convex optimization algorithm with a convergence rate of O(1/k), where k is the number of calls to the oracle. This algorithm yields subsolutions of the HJB equation that approximate the value function and provide a lower bound on the optimal time. We study the closed-loop control built on the obtained approximate value functions, and we give theoretical guarantees on its performance depending on the approximation error for the value function. We show promising numerical results for three non-polynomial systems with up to 6 state variables and 5 control variables.
Publikationsart: report
Sprache: English
Relation: info:eu-repo/semantics/altIdentifier/arxiv/2307.00857; ARXIV: 2307.00857
Verfügbarkeit: https://hal.science/hal-04145402
https://hal.science/hal-04145402v2/document
https://hal.science/hal-04145402v2/file/oustry_tacchi_mintimecontrol_230706.pdf
Rights: http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
Dokumentencode: edsbas.CD32D3BC
Datenbank: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://hal.science/hal-04145402#
    Name: EDS - BASE (s4221598)
    Category: fullText
    Text: View record from BASE
  – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=Oustry%20A
    Name: ISI
    Category: fullText
    Text: Nájsť tento článok vo Web of Science
    Icon: https://imagesrvr.epnet.com/ls/20docs.gif
    MouseOverText: Nájsť tento článok vo Web of Science
Header DbId: edsbas
DbLabel: BASE
An: edsbas.CD32D3BC
RelevancyScore: 994
AccessLevel: 3
PubType: Report
PubTypeId: report
PreciseRelevancyScore: 994.3056640625
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Minimal-time nonlinear control via semi-infinite programming
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Oustry%2C+Antoine%22">Oustry, Antoine</searchLink><br /><searchLink fieldCode="AR" term="%22Tacchi%2C+Matteo%22">Tacchi, Matteo</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: Optimization at LIX (OptimiX)<br />Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX)<br />École polytechnique (X)<br />Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)<br />Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)<br />École nationale des ponts et chaussées (ENPC)<br />GIPSA - Modelling and Optimal Decision for Uncertain Systems (GIPSA-MODUS)<br />GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD)<br />Grenoble Images Parole Signal Automatique (GIPSA-lab)<br />Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)<br />Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)<br />Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab)<br />Université Grenoble Alpes (UGA)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <i>https://hal.science/hal-04145402 ; 2025</i>.
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: CCSD
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2025
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: Université Grenoble Alpes: HAL
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Nonlinear+control%22">Nonlinear control</searchLink><br /><searchLink fieldCode="DE" term="%22Minimal+time+control%22">Minimal time control</searchLink><br /><searchLink fieldCode="DE" term="%22Weak+formulation%22">Weak formulation</searchLink><br /><searchLink fieldCode="DE" term="%22Semi-infinite+programming%22">Semi-infinite programming</searchLink><br /><searchLink fieldCode="DE" term="%22[MATH%2EMATH-OC]Mathematics+[math]%2FOptimization+and+Control+[math%2EOC]%22">[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values of which converge to the value of the control problem. These semi-infinite programs are increasing restrictions of the dual of the nonlinear control problem, which is a maximization problem over the subsolutions of the Hamilton-Jacobi-Bellman (HJB) equation. Our approach is compatible with generic dynamical systems and state constraints. Specifically, we use an oracle that, for a given differentiable function, returns a point at which the function violates the HJB inequality. We solve the semi-infinite programs using a classical convex optimization algorithm with a convergence rate of O(1/k), where k is the number of calls to the oracle. This algorithm yields subsolutions of the HJB equation that approximate the value function and provide a lower bound on the optimal time. We study the closed-loop control built on the obtained approximate value functions, and we give theoretical guarantees on its performance depending on the approximation error for the value function. We show promising numerical results for three non-polynomial systems with up to 6 state variables and 5 control variables.
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: report
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: info:eu-repo/semantics/altIdentifier/arxiv/2307.00857; ARXIV: 2307.00857
– Name: URL
  Label: Availability
  Group: URL
  Data: https://hal.science/hal-04145402<br />https://hal.science/hal-04145402v2/document<br />https://hal.science/hal-04145402v2/file/oustry_tacchi_mintimecontrol_230706.pdf
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.CD32D3BC
PLink https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.CD32D3BC
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Nonlinear control
        Type: general
      – SubjectFull: Minimal time control
        Type: general
      – SubjectFull: Weak formulation
        Type: general
      – SubjectFull: Semi-infinite programming
        Type: general
      – SubjectFull: [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
        Type: general
    Titles:
      – TitleFull: Minimal-time nonlinear control via semi-infinite programming
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Oustry, Antoine
      – PersonEntity:
          Name:
            NameFull: Tacchi, Matteo
      – PersonEntity:
          Name:
            NameFull: Optimization at LIX (OptimiX)
      – PersonEntity:
          Name:
            NameFull: Laboratoire d'informatique de l'École polytechnique Palaiseau (LIX)
      – PersonEntity:
          Name:
            NameFull: École polytechnique (X)
      – PersonEntity:
          Name:
            NameFull: Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
      – PersonEntity:
          Name:
            NameFull: Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS)
      – PersonEntity:
          Name:
            NameFull: École nationale des ponts et chaussées (ENPC)
      – PersonEntity:
          Name:
            NameFull: GIPSA - Modelling and Optimal Decision for Uncertain Systems (GIPSA-MODUS)
      – PersonEntity:
          Name:
            NameFull: GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD)
      – PersonEntity:
          Name:
            NameFull: Grenoble Images Parole Signal Automatique (GIPSA-lab)
      – PersonEntity:
          Name:
            NameFull: Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)
      – PersonEntity:
          Name:
            NameFull: Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)
      – PersonEntity:
          Name:
            NameFull: Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab)
      – PersonEntity:
          Name:
            NameFull: Université Grenoble Alpes (UGA)
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-locals
              Value: edsbas
            – Type: issn-locals
              Value: edsbas.oa
          Titles:
            – TitleFull: https://hal.science/hal-04145402 ; 2025
              Type: main
ResultId 1