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Newton-Based Extremum Seeking: a Second-Order Lie Bracket Approximation Approach

par Labar, Christophe ;Garone, Emanuele ;Kinnaert, Michel ;Ebenbauer, Christian
Référence Automatica, 105, page (356-367)
Publication Publié, 2019-03-01

Article révisé par les pairs

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Résumé :

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.