Solution of a differential game formulation of military air operations by the method of characteristics

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. Control variables are 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. The Hamiltonian in this nonlinear formulation can be explicitly optimized 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