Unbiased Extremum Seeking Based on Lie Bracket Averaging
arxiv(2024)
摘要
Extremum seeking is an online, model-free optimization algorithm
traditionally known for its practical stability. This paper introduces an
extremum seeking algorithm designed for unbiased convergence to the extremum
asymptotically, allowing users to define the convergence rate. Unlike
conventional extremum seeking approaches utilizing constant gains, our
algorithms employ time-varying parameters. These parameters reduce perturbation
amplitudes towards zero in an asymptotic manner, while incorporating
asymptotically growing controller gains. The stability analysis is based on
state transformation, achieved through the multiplication of the input state by
asymptotic growth function, and Lie bracket averaging applied to the
transformed system. The averaging ensures the practical stability of the
transformed system, which, in turn, leads to the asymptotic stability of the
original system. Moreover, for strongly convex maps, we achieve exponentially
fast convergence. The numerical simulations validate the feasibility of the
introduced designs.
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