  A fundamental concern in progressing Airborne Wind Energy (AWE) operations
towards commercial success, is guaranteeing that safety requirements placed on
the systems are met. Due to the high dimensional complexity of AWE systems,
however, formal mathematical robustness guarantees become difficult to compute.
We draw on research from Hamilton-Jacobi (HJ) reachability analysis to compute
the optimal control policy for tracking a flight path, while enforcing safety
constraints on the system. In addition, the zero-sublevel set of the computed
value function inherent in HJ reachability analysis indicates the backward
reachable set, the set of states from which it is possible to safely drive the
system into a target set within a given time without entering undesirable
states. Furthermore, we derive a switching law, such that the safety controller
can be used in conjunction with arbitrary least restrictive controllers to
provide a safe hybrid control law. In such a setup, the safety controller is
only activated when the system approaches the boundary of its maneuverability
envelope. Such a hybrid control law is a notable improvement over existing
robust control approaches that deteriorate performance by assuming the
worst-case environmental and system behavior at all times. We illustrate our
results via extensive simulation-based studies.
