Secondary Control for the Safety of LTI Systems under Attacks

We consider the problem of controller design for linear time-invariant cyber-physical systems (CPSs) controlled over a network. Specifically, we adopt the set-up that a controller has already been designed to stabilize the plant. However, the closed loop system may be subject to actuator and sensor attacks. We first perform a reachability analysis to see the effect of potential attacks. To further ensure the safety of the states of the system, we choose a subset of sensors that can be locally secured and made free of attacks. Using these limited resources, an extra controller is designed to enhance the safety of the new closed loop. The safety of the system will be characterized by the notion of safe sets. Lyapunov based analysis will be used to derive sufficient conditions that ensure the states always stay in the safe set. The conditions will then be stated as convex optimization problems which can be solved efficiently. Lastly, our theoretical results are illustrated through numerical simulations.