Point-wise Extremum Seeking Control Scheme Under Repeatable Control Environment

In this paper, a point-wise extremum seeking control scheme is proposed to seek an optimal trajectory of a time-varying static map under a repeatable control environment. At each time instant, the extremum seeking scheme seeks an optimal value in the optimal trajectory. Under some conditions, it is shown that by tuning the controller parameters properly, the output of the system semi-globally practically uniformly converges to an arbitrarily small neighborhood of the optimal trajectory from an arbitrary initial trajectory. It also shows when a weaker assumption is used, the point-wise extremum seeking controller still ensures that the output converges to the neighborhood of the optimal trajectory when the initial trajectory is sufficiently close to the optimal one.