Solution of a Differential Game Formulation of Military Air Operations by the Method of Characteristics |
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| Authors: | I N Katz H Mukai H Schättler M Zhang M Xu |
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| Institution: | (1) Professor, Department of Electrical and Systems Engineering, Washington University, St. Lousis, Missouri, USA;(2) Research Associate, Department of Electrical and Systems Engineering, Washington University, St. Lousis, Missouri, USA;(3) Graduate Student, Department of Electrical and Systems Engineering, Washington University, St. Lousis, Missouri, USA |
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| 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.Effort sponsored by the Defense Advanced Research
Projects Agency (DARPA) and Air Force Research Laboratory, Air Force
Material Command, USAF, under Agreement F30602-99-2-0551. A shorter version of this paper appeared in the Proceedings of the 2001 American Control Conference, pp. 168--175, 2001. |
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| Keywords: | Differential games method of characteristics military air operations |
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