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Differential‐game examination of optimal time‐sequential fire‐support strategies

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  • James G. Taylor

Abstract

Optimal time‐sequential fire‐support strategies are studied through a two‐person zero‐sum deterministic differential game with closed‐loop (or feedback) strategies. Lanchester‐type equations of warfare are used in this work. In addition to the max‐min principle, the theory of singular extremals is required to solve this prescribed‐duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force‐level‐dependent optimal fire‐support strategies with the attacker's optimal fire‐support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester‐type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.

Suggested Citation

  • James G. Taylor, 1978. "Differential‐game examination of optimal time‐sequential fire‐support strategies," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(2), pages 323-355, June.
  • Handle: RePEc:wly:navlog:v:25:y:1978:i:2:p:323-355
    DOI: 10.1002/nav.3800250213
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