3-DIMENSIONAL AIR-TO-AIR MISSILE TRAJECTORY SHAPING

Open-loop range/energy/time optimal trajectories are synthesized for a three-dimensional point-mass model of a boost-sustain-coact air-to-ai r missile (AAM) in atmospheric flight. Boundaries of attainable sets f or various fixed flight times are obtained by numerically solving the associated two-point boundary value problem (TPBVP) implied by the fir st-order necessary conditions of optimal control. The attainable set p rovides insight into the range capabilities of the missile in all dire ctions in the down range-cross range plane for prescribed end-game ene rgy requirements. Necessary and sufficient conditions for optimality a re checked for candidate extremals. A new governing matrix differentia l equation and suitable boundary conditions are derived to check for c onjugate points along regular or regularized extremals. This new matri x differential equation overcomes the difficulty of standard matrix Ri ccati equations for conjugate point testing, which have components who se values go to infinity even in the absence of conjugate points. The open loop solutions presented in this study can be utilized to generat e a neighboring near-optimal guidance scheme.