Reachability calculation for aircraft maneuver using Hamilton-Jacobi function

To help the pilots make decisions for aircraft maneuvers, a reachability analysis method using Hamilton-Jacobi partial differential equation is proposed in this paper. The aircraft maneuver is divided into several phases based on the key points. The restricted set of aircraft states at each key point is seen as the target set, and then a reachable set can be obtained by solving the Hamilton-Jacobi partial differential equation. The target set and the reachable set are both described by zero level set. For the three dimensional dynamical model of the aircraft, the reachable set of each key point and the feasible state space of the whole loop maneuver have been achieved. In order to make the analysis results more easy to use in practice, a four dimensional dynamical model of the aircraft which takes the rate of the angle of attack as the control parameter is formulated. Based on the four dimensional dynamical model, the reachable set is analyzed by means of the proposed method.