Safe Set Protection and Restoration for Unimpaired and Impaired Aircraft

The flight envelope can be viewed as a set within the state space of an aircraft. For various safety considerations an aircraft is required to remain within its prescribed flight envelope. The safe set is the largest controlled invariant set within the flight envelope. Thus, if an aircraft is to remain within its envelope it must stay within the safe set. When an aircraft is impaired, e.g., a jammed elevator or an engine loss, the safe set shrinks as would be expected. In this paper we consider strategies to prevent the aircraft from departing the safe set the envelope protection problem and strategies to restore the aircraft to a desired trim point within the safe set should it find itself outside the safe set the envelope restoration problem. Note that an aircraft may be driven outside of the safe set by a disturbance, a loss-of-control incident, or by a component failure in which the safe set shrinks. The problems of envelope protection and restoration are substantially different. Envelope protection requires avoiding close proximity to certain critical boundary segments of the safe set. Restoration is more straightforward involving steering the aircraft to a target trim condition along trajectories that minimize the excursion from the flight envelope. Precise formulations of both problems will be given and alternative solutions will be compared. Examples are given using a model derived from the the longitudinal dynamics of NASA’s Generic Transport Model.