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**Two-target game model of an air combat with fire-and-forget all-aspect missiles.**
*(English)*
Zbl 0662.90103

An air combat duel between similar aggressive fighter aircract, both equipped with the same type of guided missiles is formulated as a two- target differential game using the dynamic model of the game of two identical cars. Each of the identical target sets represents the effective firing envelope of an all-aspect fire-and-forget air-to-air missile. The firing range limits depend on the target aspect angle and are approximated by analytical functions. The maximum range, computed by taking into account the optimal missile avoidance maneuver of the target, determines the no-escape firing envelope. The solution consists of the decomposition of the game space into four regions: the respective winning zones of the two opponents, the draw zone, and the region where the game terminates by a mutual kill. The solution provides a new insight for future air combat analysis.

Reviewer: A.Davidovitz

### Keywords:

air combat duel; guided missiles; two-target differential game; game of two identical cars; winning zones
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\textit{A. Davidovitz} and \textit{J. Shinar}, J. Optim. Theory Appl. 63, No. 2, 133--165 (1989; Zbl 0662.90103)

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### References:

[1] | Isaacs, R.,Differential Games, R. E. Krieger Publishing Company, Huntington, New York, New York, 1975. |

[2] | Olsder, G. J., andBreakwell, J. V.,Role Determination in Aerial Dogfight, International Journal of Game Theory, Vol. 3, No. 2, pp. 47-66, 1974. · Zbl 0278.90100 |

[3] | Kelley, H. J.,A Threat Reciprocity Concept for Pursuit Evasion, Differential Games and Control Theory II, Edited by E. O. Roxin, P. T. Liu, and R. L. Sternberg, Marcel Dekker, New York, New York, 1977. |

[4] | Kelley, H. J., andLefton, L.,A Preference-Ordered Discrete Gaming Approach to Air-Combat Analysis, IEEE Transactions on Automatic Control, Vol. 23, No. 4, pp. 642-645, 1978. · Zbl 0383.90116 |

[5] | Shinar, J.,Solution Techniques for Realistic Pursuit-Evasion Games, Advances in Control and Dynamic Systems, Edited by C. T. Leondes, Academic Press, New York, New York, Vol. 17, pp. 63-124, 1981. · Zbl 0547.90106 |

[6] | Jarmark, B.,A Missile Duel between Two Aircraft, Journal of Guidance, Control, and Dynamics, Vol. 8, No. 4, pp. 508-513, 1986. |

[7] | Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969. |

[8] | Getz, W. M., andLeitmann, G.,Qualitative Differential Games with Two Targets, Journal of Mathematical Analysis and Applications, Vol. 68, No.2, pp. 421-430, 1979. · Zbl 0497.90097 |

[9] | Ardema, M. D., Heyman, M., andRajan, N.,Combat Games, Journal of Optimization Theory and Applications, Vol. 46, No. 4, pp. 391-398, 1985. · Zbl 0548.90102 |

[10] | Getz, W. M., andPachter, M.,Two-Target Pursuit-Evasion Differential Games in the Plane, Journal of Optimization Theory and Applications, Vol. 34, No. 3, pp. 383-404, 1981. · Zbl 0431.90099 |

[11] | Davidovitz, A., andShinar, J.,Eccentric Two-Target Model for Qualitative Air Combat Game Analysis, Journal of Guidance, Control, and Dynamics, Vol. 8, No. 3, pp. 325-331, 1985. |

[12] | Merz, A. W.,To Pursue or to Evade?That is the Question, Journal of Guidance Control, and Dynamics, Vol. 8, No. 2, pp. 161-166, 1985. · Zbl 0578.90107 |

[13] | Shinar, J., andDavidovitz, A.,A Two-Target Game Analysis in Line-of-Sight Coordinates, Computer and Mathematics with Applications, Vol. 13, Nos. 1-3, pp. 123-140, 1987. · Zbl 0617.90108 |

[14] | Shinar, J.,Missile Avoidance Maneuvers of Longer Duration, Technion-Israel Institute of Technology, TAE Report No. 564, 1985. |

[15] | Shinar, J., andGazit, R.,Optimal No-Escape Firing Envelopes of Guided Missiles, AIAA Paper No. 85-1960, AIAA Guidance, Navigation, and Control Conference, Snowmass, Colorado, 1985. |

[16] | Merz, A. W.,The Game of Two Identical Cars, Journal of Optimization Theory and Applications, Vol. 9, No. 5, pp. 324-343, 1972. · Zbl 0223.90035 |

[17] | Shinar, J., andDavidovitz, A.,Unified Approach for Two-Target Game Analysis, Proceedings of the 10th IFAC World Congress, Munich, Germany, pp. 65-71, 1987. |

[18] | Bernhard, P.,Corner Conditions for Differential Games, Paper Presented at the IFAC 5th World Congress, Paris, France, 1972. |

[19] | Leshem, D.,Composite Barriers and Corner Conditions in Differential Games, PhD Thesis, Department of Aeronautics and Astronautics, Stanford University, 1985. |

[20] | Peng, W. Y. S.,Controllability and Qualitative Game Transversality Conditions for Nonsmooth Targets, PhD Dissertation, University of Arizona, 1973. |

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