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Solution of a Differential Game Formulation of Military Air Operations by the Method of Characteristics

Author

Listed:
  • I. N. Katz

    (Washington University)

  • H. Mukai

    (Washington University)

  • H. Schättler

    (Washington University)

  • M. Zhang

    (Washington University)

  • M. Xu

    (Washington University)

Abstract

In this paper, we describe a zero-sum differential game formulation for the control of military air operations. The model consists of a system of nonlinear ordinary differential equations for the dynamics of the operations and a suitably chosen quadratic payoff function. The control variables are the engagement intensities and velocities, and there are constraints on the controls. The method of characteristics (based on the Pontryagin maximum principle) is used to solve the associated Hamilton-Jacobi equation. In this nonlinear formulation, the Hamiltonian can be optimized explicity with respect to the controls. Numerical simulations study the enforcement of constraints (a) by means of penalties in the payoff function or (b) explicitly. The numerical results show robustness with respect to various parameters.

Suggested Citation

  • I. N. Katz & H. Mukai & H. Schättler & M. Zhang & M. Xu, 2005. "Solution of a Differential Game Formulation of Military Air Operations by the Method of Characteristics," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 113-135, April.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:1:d:10.1007_s10957-004-1713-7
    DOI: 10.1007/s10957-004-1713-7
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    Cited by:

    1. Li, Bo & Zhang, Ranran & Jin, Ting & Shu, Yadong, 2021. "Parametric approximate optimal control of uncertain differential game with application to counter terror," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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