Functional feedback in an extremum seeking loop

We analyze the effect of functional feedback in an extremum seeking loop. Our study is motivated by a formation flight problem where the trailing aircraft experiences an outward rolling moment as the vortex effects of the leading aircraft come into play. Viewed as the extremized functional, this rolling moment feeds itself back to the lateral dynamics of the aircraft. In the initial half of the paper we impose restrictions on the curvature of the extremized functional and examine the effect under the assumption of a dynamic time-scale separation between the tracking loops of the linear dynamical system and the extremum seeking loop; in the latter half we remove both these assumptions and instead impose assumed functional forms on the extremized functional.