TY - JOUR

T1 - Barrier trajectories of a realistic missile/target pursuit-evasion game

AU - Breitner, M.

AU - Grimm, W.

AU - Pesch, H. J.

N1 - Copyright: Copyright 2004 Elsevier B.V., All rights reserved.

PY - 1991

Y1 - 1991

N2 - Presently a computer based pilot's decision aid is developed for future fighter aircraft. The objective is to increase the probability of success in the case of own attack and to improve the chance of survival in a situation of hostile attack. In the first case the firing range of a missile must be estimated by the onboard computer to pick the right launch time. In the second case the aircraft becomes the target of an adversary missile. Now, a favourable evasive maneuver must be initiated in time and controlled by an autonomous guidance algorithm. For both purposes the pursuit-evasion game concept (Isaacs [8]) applied to the missile/target encounter provides the suitable mathematical framework. The game solution indicates both the firing range of the missile and the optimal evasive maneuver of the target. First, game solutions were obtained for simplified models (e.g. linearized equations of motion (Shinar, Gutman [14]), simplified dynamics in the vertical plane (Guelman et al. [7])) or approximated with the help of singular perturbation technique (Shinar, Gazit [13]). The game solution also shows the optimal missile guidance. If one is only interested in this aspect a one sided optimal control formulation is sufficient. This approach was applied to the complete point mass model in the vertical plane to maximize the missile's range subject to the condition that there remains enough energy for the final pursuit of the target (Kumar et al. [11]). The final pursuit phase itself was not explicitly considered in the study. The optimal trajectories of [11] served as reference flight paths in a closed-loop missile guidance law (Kumar et al. [10]). The intention of the present paper is to resume the differential game approach and to combine it with a dynamic model containing realistic approximations for thrust and drag. The objective is to determine barrier trajectories in the vertical plane under the assumption that complete state and model information is available to each vehicle. Initial speed and altitude of the target aircraft are systematically varied within the flight envelope. For the missile two different launch positions are considered. The barrier trajectories are computed numerically by solving multipoint boundary value problems derived from the necessary conditions for the barrier. As a by-product, the dependence of the firing range on the altering initial values is obtained. Thus, the results draw a detailed picture of the firing envelope for the underlying vehicle models.

AB - Presently a computer based pilot's decision aid is developed for future fighter aircraft. The objective is to increase the probability of success in the case of own attack and to improve the chance of survival in a situation of hostile attack. In the first case the firing range of a missile must be estimated by the onboard computer to pick the right launch time. In the second case the aircraft becomes the target of an adversary missile. Now, a favourable evasive maneuver must be initiated in time and controlled by an autonomous guidance algorithm. For both purposes the pursuit-evasion game concept (Isaacs [8]) applied to the missile/target encounter provides the suitable mathematical framework. The game solution indicates both the firing range of the missile and the optimal evasive maneuver of the target. First, game solutions were obtained for simplified models (e.g. linearized equations of motion (Shinar, Gutman [14]), simplified dynamics in the vertical plane (Guelman et al. [7])) or approximated with the help of singular perturbation technique (Shinar, Gazit [13]). The game solution also shows the optimal missile guidance. If one is only interested in this aspect a one sided optimal control formulation is sufficient. This approach was applied to the complete point mass model in the vertical plane to maximize the missile's range subject to the condition that there remains enough energy for the final pursuit of the target (Kumar et al. [11]). The final pursuit phase itself was not explicitly considered in the study. The optimal trajectories of [11] served as reference flight paths in a closed-loop missile guidance law (Kumar et al. [10]). The intention of the present paper is to resume the differential game approach and to combine it with a dynamic model containing realistic approximations for thrust and drag. The objective is to determine barrier trajectories in the vertical plane under the assumption that complete state and model information is available to each vehicle. Initial speed and altitude of the target aircraft are systematically varied within the flight envelope. For the missile two different launch positions are considered. The barrier trajectories are computed numerically by solving multipoint boundary value problems derived from the necessary conditions for the barrier. As a by-product, the dependence of the firing range on the altering initial values is obtained. Thus, the results draw a detailed picture of the firing envelope for the underlying vehicle models.

UR - http://www.scopus.com/inward/record.url?scp=0025748315&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0025748315

VL - 156

SP - 48

EP - 57

JO - Lecture Notes in Control and Information Sciences

JF - Lecture Notes in Control and Information Sciences

SN - 0170-8643

T2 - 4th International Symposium on Differential Games and Applications

Y2 - 9 August 1990 through 10 August 1990

ER -