Modeling and optimizing military air operations

Dynamic programming has recently received significant attention as a possible technology for formulating control commands for decision makers in an extended complex enterprise that involves adversarial behavior. Enterprises of this type are typically modeled by a nonlinear discrete time dynamic system. The state is controlled by two decision makers, each with a different objective function and different hierarchy of decision making structure. To illustrate this enterprise, we derive a state space dynamic model of an extended complex military operation that involves two opposing forces engaged in a battle. The model assumes a number of fixed targets that one force is attacking and the other is defending. Due to the number of control commands, options for each force, and the steps during which the two forces could be engaged, the optimal solution for such a complicated dynamic game over all stages is computationally extremely difficult, if not impossible, to propose. As an alternative, we propose an expeditious suboptimal solution for this type of adversarial engagement. We discuss a solution approach where the decisions are decomposed hierarchically and the task allocation is separate from cooperation decisions. This decoupled solution, although suboptimal in the global sense, is useful in taking into account how fast the decisions should be in the presence of adversaries. An example scenario illustrating this military model and our solution approach is presented.