Victoria Grushkovskaya, Sameh Eisa · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27239 · open-access PDF
Dalam makalah ini, kami memanfaatkan baru-baru ini dikembangkan umum-tinggi-order Lie bracket approximation teori dan kerangka kerja untuk sistem kontrol-affine untuk menunjukkan bahwa kita dapat merancang ekstremum mencari (ES) sistem yang menggabungkan aliran berdasarkan: (i) pertama-order Lie bracket approximation, yang memberikan tingkat konvergensi eksponensial untuk fungsi objektif persegi dan tingkat konvergensi polinomial untuk fungsi objektif non-persegi; dan (ii) lebih tinggi-order Lie bracket approximation, yang memberikan tingkat konvergensi eksponensial dekat minimizer bahkan jika fungsi objektif adalah non-persegi (yaitu, melipatgandakan fungsi objektif non-persegi).
Machine translation (Meta M2M100); the English original follows.
In this paper, we leverage the recently developed general higher-order Lie bracket approximation theory and framework for control-affine systems to show that we can design extremum seeking (ES) systems that combine flows based on: (i) first-order Lie bracket approximation, which provide an exponential convergence rate for quadratic objective functions and polynomial convergence rate for non-quadratic objective functions; and (ii) higher-order Lie bracket approximation, which provide exponential convergence rate near the minimizer even if the objective function is non-quadratic (i.e., flatter a
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