Gradient approximation and extremum seeking via needle variations
Provides theoretical insight into gradient approximation for control systems, but the practical impact is incremental.
The paper derives a gradient approximation scheme using needle-shaped inputs, showing that the system moves along a weighted averaged gradient, and presents a new optimization algorithm combining heavy ball and Nesterov's methods.
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.