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Newton-based extremum seeking: A second-order Lie bracket approximation approach.
- Source :
-
Automatica . Jul2019, Vol. 105, p356-367. 12p. - Publication Year :
- 2019
-
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]
Details
- Language :
- English
- ISSN :
- 00051098
- Volume :
- 105
- Database :
- Academic Search Index
- Journal :
- Automatica
- Publication Type :
- Academic Journal
- Accession number :
- 137030464
- Full Text :
- https://doi.org/10.1016/j.automatica.2019.04.010