Multi-Agent Deployment Around a Source in the Plane Using Biased Extremum Seeking

We introduce a concept in extremum seeking, namely biased extremum seeking, which adaptively finds a set point corresponding to a prescribed bias of the value that optimizes an unknown static map. To this end, a loop consists of a product of the estimate of the Hessian of the map and the desired bias is added to the gradient based extremum seeking. Both constant bias and slowly time-varying bias are considered. As an application, the proposed scheme is used to make a group of fully actuated agents finding the source of a measurable signal in the plane while simultaneously achieving a formation deployment around it.