Title :
Solution of a differential game formulation of military air operations by the method of characteristics
Author :
Katz, I.N. ; Mukai, H. ; Schättler, H. ; Zhang, Mingjun
Author_Institution :
Washington Univ., St. Louis, MO, USA
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. 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
Keywords :
differential games; maximum principle; military systems; nonlinear differential equations; Hamilton-Jacobi equation; Hamiltonian optimization; Pontryagin maximum principle; characteristics method; differential game formulation; engagement intensities; military air operations; nonlinear formulation; nonlinear ordinary differential equations; payoff function penalties; quadratic payoff function; robustness; velocities; zero-sum differential game; Aircraft; Differential equations; Mathematical model; Missiles; Nonlinear dynamical systems; Nonlinear equations; Numerical simulation; Robustness; Velocity control;
Conference_Titel :
American Control Conference, 2001. Proceedings of the 2001
Conference_Location :
Arlington, VA
Print_ISBN :
0-7803-6495-3
DOI :
10.1109/ACC.2001.945535
