Estimation of safe flight envelope considering manoeuver overload based on cost-limited reachable set

Depending on magnitude and duration, any manoeuvering overload can damage the structure of an aircraft and adversely affect the pilot’s concentration and reaction time. These are all threats to flight safety. The flight safety envelope estimation method based on the classical reachable set cannot take into account the effect of manoeuvering overload. To overcome this limitation, a generalized reachable set known as a cost-limited reachable set is introduced into the computation of flight safety envelopes in this paper. It differs from the classical reachable set in that the performance index of the system can be set as the time integral of a running cost, and it can discuss the ability to reach the trim set before the performance index grows to the admissible cost. When computing the flight safety envelope, the running cost is set as a weighted sum of time consumption and manoeuver overload factor, and the flight safety envelope is defined as a cost-limited reachable set of the trim set. The flight safety envelopes and optimal control laws under the different weight of manoeuver overload factors are analyzed.