Constraining Attackers and Enabling Operators via Actuation Limits

While all physical systems have bounds on actuator capabilities, imposing artificial limits on the inputs of a system can reduce potential damage caused by system disturbances, including strategic attacks, by avoiding dangerous states. These artificial bounds may, however, affect the performance of the system and may make states required for operation unreachable. To solve this conflict, we construct Linear Matrix Inequalities (LMIs) and exploit some unexpected structure in the solution space to design limits on inputs such that the reachable set of the system state includes desired operation states and avoids dangerous states. We demonstrate the performance of our methods through a numerical example and case study.