Title: Capture set computation of an optimally guided missile
Authors: Tuomas Raivio
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 HUT, FINLAND

Date: March 2000
Status: Systems Analysis Laboratory Research Report E5 March 2000
Abstract: The paper presents a game theoretical approach for numerically computing the capture set of an optimally guided medium range air-to-air missile against a given target. Realistic point mass models are used, as long flight times prevent simplifications like coplanarity or constant speed target. The capture set is obtained by constructing saddle point trajectories on its boundary, or the barrier, numerically. Instead of solving a game of kind, the trajectories are identified by setting up an auxiliary game of degree. The necessary conditions of the auxiliary game are shown to coincide with those of the game of kind. The game of degree is solved from systematically varied initial states with a decomposition method that does not require setting up or solving the necessary conditions. Examples are calculated for a generic fighter and a missile.
Keywords: Pursuit-evasion game, game of kind, optimal control, discretization, missile guidance, missile avoidance.