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Newton-based extremum seeking: A second-order Lie bracket approximation approach.

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Title: Newton-based extremum seeking: A second-order Lie bracket approximation approach.
Authors: Labar, Christophe1 (AUTHOR) chlabar@ulb.ac.be, Garone, Emanuele1 (AUTHOR) egarone@ulb.ac.be, Kinnaert, Michel1 (AUTHOR) michel.kinnaert@ulb.ac.be, Ebenbauer, Christian2 (AUTHOR) ce@ist.uni-stuttgart.de
Source: Automatica. Jul2019, Vol. 105, p356-367. 12p.
Subjects: Hessian matrices, Matrix inversion, Cost functions, Mathematical functions, Dynamical systems, Brackets
Abstract: In this paper, we present novel multi-variable Newton-based extremum seeking systems, based on Lie bracket approximation methods. More precisely, we consider cost functions with an unknown mathematical description, but whose value can be measured on-line. We propose extremum seeking systems that approximate the Newton-based optimization law, by combining the on-line measurement of the cost with time-periodic excitation signals. The inversion of the Hessian matrix is avoided by introducing a first order dynamical system, whose output approximates the Newton step. This provides practical robustness with respect to ill-conditioned Hessian matrices. Semi-global stability properties of the proposed schemes are demonstrated both for static cost functions and for cost functions associated with a general non-linear dynamical system. The effectiveness of the approach is shown in simulations. [ABSTRACT FROM AUTHOR]
Copyright of Automatica is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubTypeId: academicJournal
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  Data: <searchLink fieldCode="JN" term="%22Automatica%22">Automatica</searchLink>. Jul2019, Vol. 105, p356-367. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Hessian+matrices%22">Hessian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+inversion%22">Matrix inversion</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Brackets%22">Brackets</searchLink>
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  Data: In this paper, we present novel multi-variable Newton-based extremum seeking systems, based on Lie bracket approximation methods. More precisely, we consider cost functions with an unknown mathematical description, but whose value can be measured on-line. We propose extremum seeking systems that approximate the Newton-based optimization law, by combining the on-line measurement of the cost with time-periodic excitation signals. The inversion of the Hessian matrix is avoided by introducing a first order dynamical system, whose output approximates the Newton step. This provides practical robustness with respect to ill-conditioned Hessian matrices. Semi-global stability properties of the proposed schemes are demonstrated both for static cost functions and for cost functions associated with a general non-linear dynamical system. The effectiveness of the approach is shown in simulations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Automatica is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.automatica.2019.04.010
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 356
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      – SubjectFull: Hessian matrices
        Type: general
      – SubjectFull: Matrix inversion
        Type: general
      – SubjectFull: Cost functions
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Brackets
        Type: general
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      – TitleFull: Newton-based extremum seeking: A second-order Lie bracket approximation approach.
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            NameFull: Garone, Emanuele
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            NameFull: Kinnaert, Michel
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            – D: 01
              M: 07
              Text: Jul2019
              Type: published
              Y: 2019
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