Abstract
The paper deals with differential game models of one-versus-one air combat. After a brief retrospection to classical pursuit-evasion game approaches recently introduced two-target game formulations are addressed. The possible complexity of the qualitative solution is pointed out. It results from the fact that two players need not be able to achieve the same outcome from the same initial position. The paper concentrates on two recently published quantitative approaches to define strategies for the winning player. The "combat game" is an extension of the classical game of degree. "Pareto-optimal security strategies" have their origin in n-person game theory. Finally the design of "reprisal strategies" to exploit nonoptimal behaviour of the opponent is outlined.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Literature
Ardema, M.D., Heymann, M., Rajan, N., "Analysis of a Combat Problem: The Turret Game", Journal of Optimization Theory and Applications, Vol. 54, No. 1, July 1987.
Ardema, M.D., Heymann, M., Rajan, N., "Combat Games", Journal of Optimization Theory and Applications, Vol. 46, No. 4, pp. 391–398, 1985.
Basar, T., Olsder, G.J., "Dynamic Noncooperative Game Theory", Academic Press, 1982.
Blaquiere, A., Gerard, F., Leitmann, G., "Quantitative and Qualitative Games", Academic Press, 1969.
Breakwell, J.V., Merz, A.W., "Minimum Required Capture Radius in a Coplanar Model of the Aerial Combat Problem", AIAA Journal, Vol. 15, No. 8, August 1977, pp. 1089–1094.
Bulirsch, R., "Die Mchrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung", Report of the Carl-Cranz-Gesellschaft, Heidelberg, 1971. Reprint: Munich University of Technology, Mathematical Institute, Munich, 1985.
Davidovitz, A., Shinar, J., "Two-Target Game Model of an Air Combat with Fire-and-Forget All-Aspect Missiles", Journal of Optimization Theory and Applications, Vol. 63, No. 2, Nov. 1989, pp. 133–166.
Getz, W.M., Leitmann, G., "Qualitative Differential Games with Two Targets", Journal of Mathematical Analysis and Applications, Vol. 68, pp. 421–430, 1979.
Getz, W.M., Pachter, M., "Two-Target Pursuit-Evasion Differential Games in the Plane", Journal of Optimization Theory and Applications, Vol. 34, pp. 383–403, 1981.
Ghose, D., Prasad, U.R., "Analysis of Security Strategies for a Two-Traget Game", Proceedings of the AIAA Guidance, Navigation & Control Conference, Boston, Ma., August 14–16, 1989.
Ghose, D., Prasad, U.R., "Solution Concepts in Two-Person Multicriteria Games", Journal of Optimization Theory and Applications, Vol. 63, No. 2, pp. 167–189, Nov. 1989.
Grimm, W., Prasad, U.R., Well, K.H., "Open-Loop Guidance for Prelaunch Maneuvering in Medium Range Air Combat", Proc. of the 27th IEEE Conference on Decision and Control, Austin, Texas, pp. 1442–1447, Dec. 1988.
Guelman, M., Shinar, J., Green, A., "Qualitative Study of a Planar Pursuit Evasion Game in the Atmosphere", Proc. of the AIAA Guidance, Navigation and Control Conference, Minneapolis, Minnesota, August 15–17, 1988.
Heymann, M., Rajan, N., Ardema, M.D., "On Optimal Strategies in Event-Constrained Differential Games", Proc. of the 24th IEEE Conference on Decision and Control, Fort Lauderdale, Florida, pp. 1115–1118, Dec. 1985.
Isaacs, R., "Differential Games", Wiley, New York, 1965.
Järmark, B.S.A., "A Missile Duel between Two Aircraft", Journal of Guidance and Control, Vol. 8, No. 4, pp. 508–513.
Järmark, B.S.A., "Closed-Loop Controls for Pursuit-Evasion Problems Between Two Aircraft", Presented at the Second International Symposium on Differential Game Applications, Williamsburg, Virginia, USA, August 21–22, 1986.
Järmark, B.S.A., "Differential Dynamic Programming in Differential Games", Control and Dynamic Systems, Vol. 17, edited by C.T. Leondes, Academic Press, New York, 1981.
Järmark, B.S.A., Merz, A.W., Breakwell, J.V., "The Variable-Speed Tail-Chase Aerial Combat Problem", Journal of Guidance and Control, Vol. 4, May–June 1981, pp. 323–328.
Kelley, H.J., "A Threat-Reciprocity Concept for Pursuit/Evasion", In: Differential Games and Control Theory II, Roxin, E.O., Liu, P.-T., Sternberg, R.L., Eds., Lecture Notes in Pure and Applied Mathematics, Vol. 30. New York: Marcel Dekker, 1977.
Kelley, H.J., Cliff, E.M., Lefton, L., "Reprisal Strategies in Pursuit Games", Journal of Guidance and Control, Vol. 3, pp. 257–260.
Kelley, H.J., Lefton, L., "A Preference-Ordered Discrete-Gaming Approach to Air-Combat Analysis", IEEE Transactions on Automatic Control, Vol. AC-23, No. 4, August 1978.
Kelley, H.J., Lefton, L., "Calculation of Differential-Turning Barrier Surfaces", Journal of Spacecraft and Rockets, Vol. 14, No. 2, Feb. 1977, pp. 87–95.
Merz, A.W., Hague, D.S., "Coplanar Tail-Chase Aerial Combat as a Differential Game", AIAA Journal, Vol. 15, No. 10, October 1977.
Moritz, K., Polis, R., Well, K.H., "Pursuit-Evasion in Medium Range Air Combat Scenarios", Comp. Math. Appl., Vol. 13, No. 1/3, pp. 167–180, 1987.
Oberle, H.J., Grimm, W., "BNDSCO — A Program for the Numerical Solution of Optimal Control Problems", Internal Report No. 515-89/22, Institute for Flight Systems Dynamics, DLR, Oberpfaffenhofen, FRG, 1989.
Prasad, U.R., Ghose, D., "Bicriterion Differential Games with Qualitative Outcomes", Private communication, 1990.
Prasad, U.R., Grimm, W., Berger, E.G., "A Feedback Guidance for Prelaunch Maneuvering in Medium-Range Air Comabt with Missiles", Proc. III. International Symposium on Differential Games and Applications, Antibes, France, June 16–17, 1988. Published in Springer Lecture Notes in Control and Information Sciences, Vol. 119, eds. T.S. Basar/P. Bernhard, pp. 86–96.
Rajan, N., Ardema, M.D., "Computation of Optimal Feedback Strategies for Interception in a Horizontal Plane", Journal of Guidance and Control, Vol. 7, No. 5, Sept.-Oct. 1984, pp. 627–629.
Rajan, N., Prasad, U.R., Rao, N.J., "Pursuit-Evasion of Two Aircraft in a Horizontal Plane", Journal of Guidance and Control, Vol. 3, No. 3, May-June 1980, pp. 261–267.
Shinar, J., "Validation of Zero-Order Feedback Strategies for Medium-Range Air-to-Air Interception in a Horizontal Plane", NASA Technical Memorandum 84237, NASA Ames Research Center, Moffett Field, California 94035, USA, April 1982.
Shinar, J., Davidovitz, A., "Unified Approach for Two-Target Game Analysis", Proc. of the 10th IFAC World Congress on Automatic Control, Vol. VIII, Munich, FRG, 1987, pp. 72–77.
Shinar, J., Negrin, M., Well, K.H., Berger, E.G., "Comparison between the Exact and an Approximate Feedback Solution for Medium Range Interception Problems", Proc. of the Joint Automatic Control Conference, Charlottesville, Va., June 17–19, 1981.
Shinar. J., Siegel, A.W., Gold, Y.I., "A Medium-Range Air Combat Game Solution by a Pilot Advisory System", Proceedings of the AIAA Guidance, Navigation and Control Conference, Boston, Ma., August 14–16, 1989.
Skowronski, J.M., Stonier, R.J., "The Barrier in a Pursuit-Evasion Game with Two Targets", Comput. Math. Applic., Vol. 13, No. 1-3, pp. 37–45, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Grimm, W., Well, K.H. (1991). Modelling air combat as differential game recent approaches and future requirements. In: Hämäläinen, R.P., Ehtamo, H.K. (eds) Differential Games — Developments in Modelling and Computation. Lecture Notes in Control and Information Sciences, vol 156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040221
Download citation
DOI: https://doi.org/10.1007/BFb0040221
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53787-8
Online ISBN: 978-3-540-47105-9
eBook Packages: Springer Book Archive