Stability Certificates for Periodic Trajectories of Controlled Power Kite Systems

Eva Ahbe

ETH Zurich

Tuesday, April 17, 2018, 11:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

State-feedback controllers are frequently employed in Airborne Wind Energy systems to follow reference flight paths. While many control approaches have lead to successful autonomous flight experiments the issue of reliably achieving a desired flight behaviour of the kite is still an open problem. In this talk we propose a procedure for obtaining certificates, i.e. formal guarantees, for the stabilizing region of a feedback controller used to stabilize a periodic trajectory as typically flown by a power generating kite. We hereby consider limit cycle stability properties tailored to model dynamics transformed into transverse coordinates. The region of attraction of the closed-loop system is numerically estimated from Lyapunov stability conditions which are formulated as semi-algebraic set containment problem. Using sum-of-squares relaxations the set containment problem is solved efficiently as a convex optimization problem consisting of a series of semi-definite programs. 
We further analyse the robustness of the controller with respect to parametric uncertainty in the model by employing contraction-based stability tools. The resulting optimization problem can be used either to maximize the bounds on the allowable parameter uncertainty or to maximize the estimate of the region of attraction given a fixed level of uncertainty.