An SMT-based approach to secure state estimation under sensor and actuator attacks

This paper addresses the problem of state estimation of a linear time-invariant system when some of the sensors or/and actuators are under adversarial attack. In our set-up, the adversarial agent attacks a sensor (actuator) by manipulating its measurement (input), and we impose no constraint on how the measurements (inputs) are corrupted. We introduce the notion of “sparse strong observability” to characterize systems for which the state estimation is possible, given bounds on the number of attacked sensors and actuators. Furthermore, we develop a secure state estimator based on Satisfiability Modulo Theory (SMT) solvers.