Safe Set Maneuverability, Restoration, and Protection for Aircraft

The safe set is the largest controlled invariant set within a prescribed region of the state space. Safe set theory has the potential to be a basis for the design of an envelope protection system but this idea is far from fully developed and there are many open areas for further research. This research will address some issues that can naturally arise in working with higher dimensional safe sets which are inherently difficult to visualize and manage. It is of interest to characterize the maneuverability within the safe set. Maneuverability performance is usually assessed by evaluating an aircraft's capability to regulate around and smoothly transition between desired steady state conditions. This research will employ a bifurcation approach to characterize the control properties of the attainable trim points within the safe set. This research will show how impairments, in the form of control constraints, can dramatically alter both the safe and trim sets and affect the manner in which the aircraft can be safely maneuvered. Maneuverability can also be assessed by studying reachability within the safe set. It will be shown by simulation that all points in the safe set are not always reachable from other points within the safe set, but that all trim points can be reached from all points within the safe set. This research also considers strategies to restore an aircraft to a desired trim point within the safe set should it find itself outside the safe set - the safe set restoration problem - and strategies to prevent the aircraft from departing the safe set - the safe set protection problem.