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Stability of Time-Invariant Extremum Seeking Control for Limit Cycle Minimization | IEEE Journals & Magazine | IEEE Xplore

Stability of Time-Invariant Extremum Seeking Control for Limit Cycle Minimization


Abstract:

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a met...Show More

Abstract:

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a method to prove the closed-loop system has an asymptotically stable limit cycle. The method is based on a perturbation theorem for maps, and, unlike existing techniques that use averaging and singular perturbation tools, it is not limited to weakly nonlinear systems. We use a typical example system to show that our method does indeed establish asymptotic stability of the limit cycle with minimal amplitude. Utilizing the example, we provide a general guide for analytic computations that are required to apply our method. The corresponding Mathematica code is available as supplementary material.
Published in: IEEE Transactions on Automatic Control ( Volume: 67, Issue: 9, September 2022)
Page(s): 5017 - 5024
Date of Publication: 09 June 2022

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