Uniform non-convex optimisation via Extremum Seeking

Abstract

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 minima. Under the assumption of a globally Lipschitz cost function, it is shown that the scheme, improved through a high-pass filter, makes the global minimiser practically stable with a global domain of attraction.