Efficient Flight Envelope Estimation for Changed Aircraft Dynamics

This report contains a study to find faster numerical methods for Hamilton-Jacobi Isaacs partial differential equations in application to model-based flight envelope estimation. This equation can be used to estimate the flight envelope through solving a reachability problem. The goal is to update the flight envelope with this method to maintain envelope protection after the occurrence of a failure. To do so the estimation methods have to become considerably faster. Useful insights have been obtained though assessing the reachable set theory associated to the problem, which permit to designate computational resources to regions of higher interest and to solve the problem with a new set of solving schemes by using the boundary value formulation of a minimal time differential game. A small literature study is held on the level set and fast marching methods. Five different techniques have been attempted to improve the computational efficiency. The applicability of a class of non-iterative schemes, known as the fast marching methods, has been evaluated both on a theoretical level as well as through simulation. The behavior of the studied methods is demonstrated on four example problems, including a simplified aircraft model. The research has found that in application to flight envelope estimation it is not feasible to initialize the reachability problem with an estimated set, or to recursively propagate a reachable set over a failure event. The integration of the differential equation with a set of trajectories was however found to be permissible. Potential applications for this technique have been identified. It was found that the boundary value formulation of the differential equation may be used provided that the system is modeled as a time-invariant system and that the initial set consists only of trimmable states. The non-iterative Fast Marching method was demonstrated not to be applicable to envelope estimation. An extension called the safe Fast Marching method was found to give accurate but incomplete reachable sets. It is recommended to consider the acceptance of sufficient rather than optimal control inputs to simplify the optimization problem. A continued investigation should be made on the iterative minimal time algorithms, in particular the iterative fast marching method and the fast sweeping method.Control & SimulationControl & OperationAerospace Engineerin