The paper deals with the optimal avoidance of a missile employing Proportional Navigation. We consider the final phase of the encounter, where the missile is initially flying with a supersonic velocity on collision course within some kilometers from the target aircraft. Both the missile and the aircraft move in three dimensions. Unlike in most previous approaches, the finite angular velocities of the aircraft as well as the constraints regarding the angle of attack are taken into account. For the resulting trajectory optimization problem we present a tailored solution method based on direct multiple shooting. To increase stability and robustness and to degrease the solution time, a multirate type integration method is used. The constraints imposed on the time derivatives of the control variables are taken into account using finite differences. Example trajectories are computed and the performance of the solution method is assessed.
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