Game formulation of multiteam target assignment and suppression mission

Abstract

Formulating control commands for decision makers in an extended complex mission that involves adversarial behavior has recently received significant attention. Missions 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 hierarchy of decision-making structure. To illustrate such a mission, 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, the 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 prove. 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 separated from cooperation decisions. This novel decoupled solution, although suboptimal in the global sense, is useful when decisions should be taken swiftly in the presence of adversaries. Some example scenarios illustrating this military model and our solution approach are presented.