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

Raivio, T., Ranta, J.

”Optimal missile avoidance trajectory synthesis in the endgame” Audience: Optimal control, air combat analysis and simulation professionals

S ystems Analysis Laboratory Helsinki University of Technology

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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

S ystems Analysis Laboratory Helsinki University of Technology

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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

S ystems Analysis Laboratory Helsinki University of Technology

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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

S ystems Analysis Laboratory Helsinki University of Technology

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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

S ystems Analysis Laboratory Helsinki University of Technology

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