Codesign for Resilience and Performance

We present two optimization approaches to minimize the impact of sensor falsification attacks in linear time-invariant systems controlled by estimate-based feedback. We accomplish this by finding observer and controller gain matrices that minimize outer ellipsoidal bounds that contain the reachable set of attack-induced states. To avoid trivial solutions, we involve a covariance-based $\Vert H\Vert _{2}$ closed-loop performance constraint. This exposes a tradeoff between system security and closed-loop performance and demonstrates that only small concessions in performance can lead to large gains in our reachability-based security metric. We provide both a nonlinear optimization based on geometric sums and a fully convexified approach formulated with linear matrix inequalities. We demonstrate the effectiveness of these tools on two numerical case studies.