Large-scale kites, flying high-force crosswind trajectories, have been proposed for wind power generation. A two phase operational cycle generates net positive power using a ground-based motor/generator. In the traction phase the kite flies a high-force trajectory while reeling out the generator-connected tethers. A low-force retraction phase reels in the tethers and returns the kite to the start of the cycle. Highly variable conditions and significant uncertainty in the dynamics pose challenges to autonomous, well-controlled flight. The control task is divided into trajectory generation and tracking components and the most uncertain parameters in the model are identified online. The control structure uses these parameters in a robust framework resulting in an experimentally verified adaptive control scheme.