In this talk we formulate the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization of cost functions on smooth Riemannian manifolds. This is done by introducing geodesic dithers in the tangent bundle of the ambient state manifolds and obtaining the extremum seeking closed loop as a perturbation of the averaged gradient system. The main results are applied to synchronization problems of agents evolving on Lie groups.
Group for Research in Decision Analysis