Optimal Control of Towing Kites

In this paper we present a challenging application of periodic optimal control. A kite that is towing a ship into a given target direction should fly optimal loops. We show how to find the maximum average tractive force by controlling the roll angle of the towing kite taking into account that the wind is increasing with the altitude over the sea. The optimal control problem for this highly nonlinear and unstable system has periodicity constraints, free initial values, and a free cycle duration. For its solution, we use MUSCOD-II, an optimal control package based on the direct multiple shooting method. Finally, we discuss the influence of an important design parameter, the effective glide ratio of the kite