1. 1 S ystems Analysis Laboratory Helsinki University of Technology Kai Virtanen, Tuomas Raivio, and Raimo P. Hämäläinen Systems Analysis Laboratory (SAL) Helsinki University of Technology (HUT) www.sal.hut.fi Optimal Pilot Decision and Flight Trajectories in Air Combat

2. 2 S ystems Analysis Laboratory Helsinki University of Technology The Project ”Dynamics and Strategy of Flight” Financed by the Finnish Air Force, initiated in 1993 Research group: –project leader prof. Raimo P. Hämäläinen –prof. Harri Ehtamo –three full-time researchers Research topics: –single aircraft performance optimization –analysis of antagonistic aerospace scenarios using differential games decision theoretical tools simulation Cooperation with Laboratory of Aerodynamics of HUT

3. 3 S ystems Analysis Laboratory Helsinki University of Technology Dynamic optimization one active actor control the dynamic system in the best possible way Differential games, game theory two actors optimization againts the worst action of the opponent Simulation multiple actors decision models of pilots Approaches for modeling air combat Utilization: - Planning of tactics - Pilot training - Performance evaluation

4. 4 S ystems Analysis Laboratory Helsinki University of Technology System model  y x h v  n u  - Describes the dynamics of aircraft and missiles - Translational (and rotational) dynamics

5. 5 S ystems Analysis Laboratory Helsinki University of Technology Control the dynamic system in the best possible way: –best = e.g., minimal time –obey given constraints: minimum altitude, stall velocity, g- forces,… Our research activities: –numerical solution methods time discretization and nonlinear programming –interactive optimization software Initial state x 0 Final state x f Dynamic optimization, optimal control

6. 6 S ystems Analysis Laboratory Helsinki University of Technology Minimum time climb

7. 7 S ystems Analysis Laboratory Helsinki University of Technology Minimum time flight in 3D

8. 8 S ystems Analysis Laboratory Helsinki University of Technology Missile assumed to use a known feedback guidance law One decision maker (aircraft) => optimal control problem –given vehicle parameters and initial states, choose aircraft controls Maximization of minimum distance Optimal missile avoidance is pursuing

9. 9 S ystems Analysis Laboratory Helsinki University of Technology Family of optimal solutions A B C D A B C D

10. 10 S ystems Analysis Laboratory Helsinki University of Technology Pursuit-evasion game Two-player zero-sum differential game with free terminal time Game of kind: When a capture is possible? => ‘Capture zone’ Game of degree: Saddle point strategies inside the Capture zone Our research activities: Numerical solution methods, applications Pursuer - Capture with minimal cost Evader - Escape if possible - Maximize the cost of capture Saddle point solution: Best possible action against the worst action of the opponent ? ? Fixed roles

11. 11 S ystems Analysis Laboratory Helsinki University of Technology Missile-aircraft setting Minimizes flight time Maximizes flight time

12. 12 S ystems Analysis Laboratory Helsinki University of Technology Maximal shooting range of a missile

13. 13 S ystems Analysis Laboratory Helsinki University of Technology One-on-one air combat game Find the best maneuvering sequence for the players with respect to the goals 1. Avoid being captured by the adversary 2. Capture the adversary by taking into account - Preferences of a pilot - Uncertainties - Dynamic decision environment - Behavior of the adversary t=  t t=0  t=  t  Two-target game Influence diagram Influence diagram game

14. 14 S ystems Analysis Laboratory Helsinki University of Technology Air combat simulation models Multiple aircraft More realistic dynamics and uncertainty models Discrete-event approach => Statistical analysis of results Our research activities: –X-Brawler Computer generated forces need a model imitating pilot decision making: Influence diagram approach Orders Commands simulation experiments

15. 15 S ystems Analysis Laboratory Helsinki University of Technology Future modeling challenges Modeling: –Improved models for flight mechanics Optimization, differential games: –Optimal control and games under increased uncertainty –Optimal feedback strategy approximation Simulation: –Optimal decisions under uncertainty –Combination of discrete-event simulation and optimization Methodological contributions are required

16. 16 S ystems Analysis Laboratory Helsinki University of Technology More information www.sal.hut.fi Selected publications: Virtanen, Raivio, and Hämäläinen, "Modeling Pilot's Sequential Maneuvering Decisions by a Multistage Influence Diagram," Journal of Guidance, Control, and Dynamics, Vol. 27, No. 4, 2004. Virtanen, Hämäläinen, and Mattila, "Team Optimal Signaling Strategies in Air Combat," IEEE Transaction on Systems, Man, and Cybernetics - Part A: Systems and Humans, accepted for publication, 2004. Ehtamo and Raivio, “On Applied Nonlinear and Bilevel Programming for Pursuit-Evasion Games,” Journal of Optimization Theory and Applications, Vol. 108, No. 1, 2001. Raivio, “Capture Set Computation of an Optimally Guide Missile,” Journal of Guidance, Control, and Dynamics, Vol. 24, no. 6, 2001 Raivio and Ehtamo, “On Numerical Solution of a Class of Pursuit-Evasion Games,” Annals of the International Society of Dynamic Games, Vol. 5, 2000. Raivio and Ehtamo, “Visual Aircraft Identification as a Pursuit-Evasion Game,” Journal of Guidance, Control and Dynamics, Vol. 23 No. 4, 2000. Virtanen, Raivio, and Hämäläinen, "Decision Theoretical Approach to Pilot Simulation," Journal of Aircraft, Vol. 36, No. 4, 1999. Virtanen, Ehtamo, Raivio, and Hämäläinen, "VIATO - Visual Interactive Aircraft Trajectory Optimization," IEEE Transaction on Systems, Man, and Cybernetics - Part C: Applications and Reviews, Vol. 29, No. 3, 1999.