Gradient approximation and extremum seeking via needle variations
Systems and Control
2016-03-15 v1 Optimization and Control
Abstract
We consider a gradient approximation scheme that is based on applying needle shaped inputs. By using ideas known from the classic proof of the Pontryagin Maximum Principle we derive an approximation that reveals that the considered system moves along a weighted averaged gradient. Moreover, based on the same ideas, we give similar results for arbitrary periodic inputs. We also present a new gradient-based optimization algorithm that is motivated by our calculations and that can be interpreted as a combination of the heavy ball method and Nesterov's method.
Keywords
Cite
@article{arxiv.1603.04314,
title = {Gradient approximation and extremum seeking via needle variations},
author = {Simon Michalowsky and Christian Ebenbauer},
journal= {arXiv preprint arXiv:1603.04314},
year = {2016}
}