Optimal control in the presence of an intelligent jammer with limited actions

We consider a dynamic zero-sum game between two players. The first player acts as a controller for a discrete time LTI plant, while the second player acts to jam the communication between the controller and the plant. The number of jamming actions is limited. We determine saddle-point equilibrium control and jamming strategies for this game under the full state, total recall information structure for both players, and show that the jammer acts according to a threshold policy at each decision step. Various properties of the threshold functions are derived and complemented by numerical simulation studies.