Robust Adaptive Extremum Seeking Control Without Persistence of Excitation: Theory to Experiment

In this article, we develop a novel adaptive extremum‐seeking control (AdESC) algorithm with robustness guarantees and without persistence of excitation (PE). Specifically, this builds on a proportional‐integral (PI)‐like parameter estimator. A zeroth‐order optimization framework is used, where the...

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Veröffentlicht in:International journal of robust and nonlinear control 2024-11
Hauptverfasser: Garg, Tushar, Basu Roy, Sayan, Vamvoudakis, Kyriakos G.
Format: Artikel
Sprache:eng
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Zusammenfassung:In this article, we develop a novel adaptive extremum‐seeking control (AdESC) algorithm with robustness guarantees and without persistence of excitation (PE). Specifically, this builds on a proportional‐integral (PI)‐like parameter estimator. A zeroth‐order optimization framework is used, where the optimizer/agent can only query the numerical value of the cost function at the current coordinate given an unmodeled bounded disturbance. Since parameter estimation plays a decisive role in the stability and convergence properties of AdESC algorithm, it is also well established in the existing literature that to ensure parameter convergence a stringent PE condition is required. Here, we eliminate the need for a stringent PE condition by utilizing a novel set of weighted integral filter dynamics, while ensuring sufficient richness using a milder condition, called initial excitation (IE). Moreover, to validate the robustness guarantees towards unmodeled bounded disturbance, a detailed Lyapunov function based analysis is performed to establish the closed‐loop stability and convergence in the form of uniform ultimate boundedness (UUB). Furthermore, an experimental study using a unicycle wheeled mobile robot (WMR) is carried out as a proof‐of‐concept considering disturbance and disturbance‐free scenarios.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.7707