Modeling and control of military operations against adversarial control

We present a nonlinear state space mathematical model for a class of dynamical systems that can serve as the basis for a simulation test bed for the investigation of enterprise control. Dynamic complex enterprises generally include multiple control agents of a decision team. In addition, the enterprise is generally imbedded in a larger environment that has competing and even hostile decision teams that affect the enterprise. In such situations it is appropriate to model an extended enterprise that includes the competing decision teams. For example an enterprise might be a military command and control hierarchy with several levels of command. If a command and control enterprise is deployed in a military operation, the enterprise states may be affected by non-friendly commands. In order to develop acceptable and even optimal control strategies, it is important to consider the effect of the adversarial controls even at the control design stage. Before these control strategies can be designed or investigated, a model for the extended enterprise "plant" is needed. This extended plant should have inputs from the competing decision team, in addition to the decision team inputs to the enterprise. In our model the command hierarchy is designated as the blue forces. The enterprise is imbedded in a larger system that includes a hostile command designated as the red forces. This extended enterprise is designated as military operations. In the paper, a discrete-time nonlinear state space model of a military operation is formulated and an example illustrating the implementation of the Nash strategies from non-zero sum game theory is presented.