Stability Verification for Periodic Trajectories of Autonomous Kite Power Systems

Abstract

State-feedback controllers are frequently employed in Airborne Wind Energy systems to follow reference flight paths. In this paper we compute the region of attraction (ROA) of path-stabilizing feedback gains around a periodic trajectory as typically flown by a power generating kite. The feedback gains are obtained from applying a time-varying periodic Linear Quadratic Regulator to the system expressed in transversal coordinates. To compute the ROA we formulate Lyapunov stability conditions which we verify by Sum-of-Squares programs. These programs are posed as an optimization problem for which we compare various definitions of the cost function representing the size of the ROA. In a numeric ..