Advertisement

Formulation and analysis of combat problems as zero-sum bicriterion differential games

  • U. R. Prasad
  • D. Ghose
Contributed Papers

Abstract

In this paper, we present a formulation and analysis of a combat game between two players as a zero-sum bicriterion differential game. Each player's twin objectives of terminating the game on his own target set, while simultaneously avoiding his opponent's target set, are quantified in this approach. The solution in open-loop pure strategies is sought from among the Pareto-optimal security strategies of the players. A specific preference ordering on the outcomes is used to classify initial events in the assured win, draw, and mutual kill regions for the players. The method is compared with the event-constrained differential game approach, recently proposed by others. Finally, a simple example of the turret game is solved to illustrate the use of this method.

Key Words

Combat games differential games bicriterion games Pareto-optimal strategies two-target games 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Isaacs, R.,Differential Games, John Wiley & Sons, New York, New York, 1965.Google Scholar
  2. 2.
    Ardema, M. D., Heymann, M., andRajan, N.,Combat Games, Journal of Optimization Theory and Applications, Vol. 46, No. 4, pp. 391–398, 1985.Google Scholar
  3. 3.
    Baron, S., Chu, K. C., Ho, Y. C., andKleinman, D. L.,A New Approach to Aerial Combat Games, NASA, Contractor Report No. CR-1626, 1970.Google Scholar
  4. 4.
    Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.Google Scholar
  5. 5.
    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.Google Scholar
  6. 6.
    Olsder, G. J., andBreakwell, J. V.,Role Determination in an Aerial Dogfight, International Journal of Game Theory, Vol. 3, No. 1, pp. 47–66, 1974.Google Scholar
  7. 7.
    Getz, W. M., andPachter, M.,Capturability in a Two-Target Game of Two Cars, AIAA Journal of Guidance and Control, Vol. 4, No. 1, pp. 15–21, 1981.Google Scholar
  8. 8.
    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. 383–403, 1981.Google Scholar
  9. 9.
    Davidowitz, 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.Google Scholar
  10. 10.
    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.Google Scholar
  11. 11.
    Heymann, M., Rajan, N., andArdema, M.,On Optimal Strategies in Event-Constrained Differential Games, Proceedings of the 24th IEEE Conference on Decision and Control, Fort Lauderdale, Florida, 1985.Google Scholar
  12. 12.
    Aggarwal, R., andLeitmann, G.,Avoidance Control, Journal of Dynamic Systems, Measurements, and Control, Vol. 94, No. 2, pp. 152–154, 1972.Google Scholar
  13. 13.
    Aggarwal, R., andLeitmann, G.,A Maxmin Distance Problem, Journal of Dynamic Systems, Measurement, and Control, Vol. 94, No. 2, pp. 155–158, 1972.Google Scholar
  14. 14.
    Warga, J.,Minimizing Variational Curves Restricted to A Preassigned Set, Transactions of the American Mathematical Society, Vol. 112, No. 3, pp. 432–455, 1964.Google Scholar
  15. 15.
    Johnson, C. D.,Optimal Control with Chebyhev Minimax Performance Index, Journal of Basic Engineering, Vol. 89, No. 2, pp. 251–262, 1967.Google Scholar
  16. 16.
    Powers, W. F.,A Chebyshev Minimax Technique Oriented to Aerospace Trajectory Optimization Problems, AIAA Journal, Vol. 10, No. 10, pp. 1291–1296, 1972.Google Scholar
  17. 17.
    Cunningham, E. P.,The Absolute Maximum Payoff in Differential Games and Optimal Control, Journal of Optimization Theory and Applications, Vol. 7, No. 4, pp. 258–286, 1971.Google Scholar
  18. 18.
    Prasad, U. R., andGhose, D.,Pareto-Optimality Concept Applied to Combat Games, Second International Symposium on Differential Game Applications, Williamsburg, Virginia, 1986.Google Scholar
  19. 19.
    Heymann, M., Ardema, M. D., andRajan, N.,A Formulation and Analysis of Combat Games, NASA, Report No. TP-2487, 1985.Google Scholar
  20. 20.
    Ho, Y. C., andOlsder, G. J.,Differential Games: Concepts and Applications, Mathematics of Conflict, Edited by M. Shubik, Elsevier Science Publishers, Amsterdam, Holland, 1983.Google Scholar
  21. 21.
    Corley, H. W.,Games with Vector Payoffs, Journal of Optimization Theory and Applications, Vol. 47, No. 4, pp. 491–498, 1985.Google Scholar
  22. 22.
    Schmitendorf, W. E., andMoriarty, G.,A Sufficiency Condition for Coalitive Pareto-Optimal Solutions, Multicriteria Decision Making and Differential Games, Edited by G. Leitmann, Plenum Press, New York, New York, 1976.Google Scholar
  23. 23.
    Schmitendorf, W. E.,Optimal Control of Systems with Multiple Criteria When Disturbances Are Present, Journal of Optimization Theory and Applications, Vol. 27, No. 1, pp. 135–146, 1979.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • U. R. Prasad
    • 1
  • D. Ghose
    • 2
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia
  2. 2.Joint Advanced Technology ProgramIndian Institute of ScienceBangaloreIndia

Personalised recommendations