Uniform quasi-convex optimisation via Extremum Seeking

The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the global minimiser to be semi-global practically stable despite the presence of local saddle points. To achieve these results, we analyse the average system associated with the extremum seeking scheme via arguments based on the Fourier series.

Automated summary

The paper investigates a well-known extremum seeking scheme and proves its uniformity properties in terms of dither signal amplitudes and cost function. These properties are then used to demonstrate that the scheme guarantees semi-global practical stability of the global minimizer even in the presence of local saddle points. To achieve these results, the average system associated with the extremum seeking scheme is analyzed using arguments based on the Fourier series.