  We investigate a linear quadratic Gaussian (LQG) tracking problem with safety
and reachability constraints in the presence of an adversary who mounts an FDI
attack on an unknown set of sensors. For each possible set of compromised
sensors, we maintain a state estimator disregarding the sensors in that set,
and calculate the optimal LQG control input at each time based on this
estimate. We propose a control policy which constrains the control input to lie
within a fixed distance of the optimal control input corresponding to each
state estimate. The control input is obtained at each time step by solving a
quadratically constrained quadratic program (QCQP). We prove that our policy
can achieve a desired probability of safety and reachability using the barrier
certificate method. Our control policy is evaluated via a numerical case study.
