Pop-up threat models for persistent area denial

Pop-up threats usually appear or disappear randomly in a battle field. If the next pop-up threat locations could be predicted it would assist a search or attack team, such as in a persistent area denial (PAD) mission, in getting a team of unmanned air vehicles (UAVs) to the threats sooner. We present a Markov model for predicting pop-up ground threats in military operations. We first introduce a general Markov chain of order n to capture the dependence of the appearance of pop-up threats at previous locations of the pop-up threats over time. We then present an adaptive approach to estimate the stationary transition probabilities of the nth order Markov models. To choose the order of the Markov chain model for a specific application, we suggest using hypothesis tests from statistical inference on historical data of pop-up threat locations. Anticipating intelligent responses from an adversary, which might change its pop-up threat deployment strategy upon observing UAV movements, we present adaptive Markov chain models using a moving horizon approach to estimate possibly abrupt changes in transition probabilities. We combine predicted and actual pop-up target locations to develop efficient cooperative strategies for networked UAVs. A theoretical analysis and simulation results are presented to evaluate the Markov model used for predicting pop-up threats. These results demonstrate the effectiveness of cooperative strategies using the combined information of threats and predicted threats in improving overall mission performance.     

Moving horizon Nash strategies for a military air operation

Dynamic game theory has recently received considerable attention as a possible technology for formulating control actions for decision makers in an extended complex enterprise that involves an adversary. Examples of such enterprises are very common in military operations. Enterprises of this type are typically modeled by a highly nonlinear discrete time dynamic system whose state is controlled by two teams of decision makers each with a different objective function and possibly with a different hierarchy of decision making. Because of the complexity of such systems, the traditional solutions from dynamic game theory that involve optimizing objective functions over the entire time horizon of the system are computationally extremely difficult, if not impossible, to derive. We discuss a solution approach where at each step the controllers limit the computation of their actions to a short time horizon that may involve only the next few time steps. This moving horizon solution, although suboptimal in the global sense, is very useful in taking into account the possible near-term control actions of the adversary. To illustrate this solution methodology, we consider an example of an extended military enterprise that involves two opposing forces engaged in a battle.     

Game-theoretic modeling and control of a military air operation

An attrition-type discrete-time dynamic model is formulated for two opposing forces, labeled Blue and Red, engaged in a military air operation. The Blue force consists of combat air units and its objective is to destroy a fixed target, such as an airport or a bridge, which Is being defended by the Red force. The Red force consists of ground troops and air defense units. We model the objective functions for each side and identify the associated constraints on the control and state variables. We employ a two-level hierarchy of command and control for each force. An example scenario illustrating the implementation of this approach using concepts from non-zero sum dynamic game theory is presented