Numerical methods of optimal control applied to air combat analysis Jukka Ranta

1. Numerical methods of optimal control applied to air combat analysisJukka Ranta Raivio, T., Ranta, J. ”Optimal missile avoidance trajectory synthesis in the endgame” Audience: Optimal control, air combat analysis and simulation professionals

2. Problem description • Aircraft pursued by a missile using Proportional Navigation feedback guidance law • Endgame analysis • final stage of the encounter: missile out of fuel and gliding at a large initial velocity • Find the controls of the aircraft that maximize the miss distance • Miss distance = minimum distance between the aircraft and the missile along the trajectories • Deterministic problem with perfect information • Open loop solution of an optimal control problem

3. Literature • Extensive literature on solving optimal control problems • in this context direct numerical methods • Simulations of missile evasion • investigation of different evasion trajectories • Trajectory optimization • model assumptions ranging from constant velocities and planar encounters to point mass

4. Ideas and Results • Modelling based on a point mass in 3 dimensions • aircraft rotation kinematics included in the model • Solution method • multiple shooting discretization • multirate integration (difference of aircraft/missile time scale) • control rate constraints using differential inclusion • resulting optimization problem solved by SQP • Results • applicability of the solution method • the solution is sensitive to the starting point

5. Publication 1st trial: J G C D • endgame, only kinematics considered • open loop solutions 2nd trial: J O T A • More emphasis on solution method • Computational performance