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arXiv · 2107.01176

Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error

Claus Danielson·Scott A. Bortoff·Ankush Chakrabarty
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Abstract

This paper presents an extremum seeking control algorithm with an adaptive step-size that adjusts the aggressiveness of the controller based on the quality of the gradient estimate. The adaptive step-size ensures that the integral-action produced by the gradient descent does not destabilize the closed-loop system. To quantify the quality of the gradient estimate, we present a batch least squares estimator with a novel weighting and show that it produces bounded estimation errors, where the uncertainty is due to the curvature of the unknown cost function. The adaptive step-size then maximizes the decrease of the combined plant and controller Lyapunov function for the worst-case estimation error. We prove that our ESC is input-to-state stable with respect to the dither signal. Finally, we demonstrate our proposed ESC through five numerical examples; one illustrative, one practical, and three benchmarks.

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Claus Danielson, Scott A. Bortoff, Ankush Chakrabarty. 2021-07-02. Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error. https://arxiv.org/abs/2107.01176

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