Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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The theory of nonzero sum differential games NZSDG is extended for a class of problems in which the nonlinear system equations have bounded control variables appearing linearly. For terminal cost functions this class of problems is shown to exhibit bang-bang type control laws with the possibility of singular controls. A condition is derived to test for continuity of the influence functions when controls switch from a nonsingular to a singular control on singular surfaces. Two generalized forms of the transversality conditions are derived for NZSDG theory extending results of Dreyfus and Isaacs. NZSDG theory is shown to be useful in modeling combat problems in which the goals of the players are not diametrically opposed. A two player and three player penetrator-interceptor problem are presented as a NZSDG. Numerical solutions for a totally singular problem are carried out to illustrate application and a typical solution.
- Operations Research
- Unconventional Warfare