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Differential Game for a Class of Warfare Dynamic Systems with Reinforcement Based on Lanchester Equation

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  • Xiangyong Chen
  • Jianlong Qiu

Abstract

This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions.

Suggested Citation

  • Xiangyong Chen & Jianlong Qiu, 2014. "Differential Game for a Class of Warfare Dynamic Systems with Reinforcement Based on Lanchester Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:837431
    DOI: 10.1155/2014/837431
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    References listed on IDEAS

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    1. Helmbold, Robert L., 1994. "Direct and inverse solution of the Lanchester square law with general reinforcement schedules," European Journal of Operational Research, Elsevier, vol. 77(3), pages 486-495, September.
    2. James G. Taylor, 1974. "Lanchester‐type models of warfare and optimal control," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 79-106, March.
    3. J. H. Engel, 1954. "A Verification of Lanchester's Law," Operations Research, INFORMS, vol. 2(2), pages 163-171, May.
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