Determination of optimal escape maneuver for automatic air collision avoidance system
空中自动防撞系统最优逃避机动的确定

We employ the optimal control theory to determine the optimal escape maneuver for the automatic air collision avoidance system. Firstly, a variable terminal-time optimal control problem with compound performance index is formulated for determining the optimal escape maneuver for automatic air collision avoidance system; and then, the terminal-time when two aircrafts are closest to each other in the approach is obtained by a quadratic curve fitting. Finally, by the maximum principle and the state equation of the aircraft, we derive the analytical solutions for the optimal roll rate and the optimal normal acceleration of the optimal escape maneuver for achieving the largest minimum separation between two aircrafts at the closest point of approach.