Control in the presence of an intelligent jammer with limited actions

In this thesis, we consider three different problems related to control using communication channel as a medium to transfer control signal in a networked control system. In particular, we are interested in control in the presence of an intelligent and strategic jammer who is maliciously altering the control signal or observation signal in the communication network connecting the controller and the plant. The first formulation considers a dynamic zero-sum game between a controller and a jammer for two different scenarios. 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, which captures the energy constraint of the jammer. In the first scenario, the state of the plant is unconstrained, while in the second scenario, the state of the plant is constrained by a threshold at all time steps, and both the jammer and the controller try to maintain the state of the plant below that threshold. We determine saddle-point equilibrium control and jamming strategies for these two games under the full state, total recall information structure for both players, and show that the jammer acts according to a threshold-based policy at each decision step. Various properties of the threshold functions are derived and complemented by numerical simulation studies. The next problem considers a model of stealthy attack on a networked control system by formulating a static zero-sum game among four players. The three players constitute a team of encoder, decoder and controller for a scalar discrete time linear plant, while the fourth player acts to flip the bits of the binary encoded observation signal of the communication channel between the plant and the controller. We are interested in characterizing the possible encoding/decoding/control defense strategies available to the controller and for simplicity, we model it for a scalar discrete time system with only one time step. We further assume that the communication channel has finite bandwidth, and that the observation and control signals have finite codelengths. We determine the saddle-point equilibrium control and jamming strategies for this game when the controller's strategy space is restricted to quantization-based policies, and show that the resulting performance compares favorably to universal lower bounds obtained from rate-distortion theory. We also provide a necessary and sufficient condition on the minimum number of bits that are required to drive the cost to zero for this one step control problem in the presence of a jammer