IMHOTEP-SMT: A Satisfiability Modulo Theory Solver For Secure State Estimation∗

This paper presents IMHOTEP-SMT, a solver for the detection and mitigation of sensor attacks in cyber-physical systems. IMHOTEP-SMT receives as inputs a description of the physical system in the form of a linear difference equation, the system input (control) signal, and a set of output (sensor) measurements that can be noisy and corrupted by a malicious attacker. The output is the solution of the secure state estimation problem, i.e., a report indicating: (i) the corrupted sensors, and (ii) an estimate of the continuous state of the system obtained from the uncorrupted sensors. Based on this estimate, it is then possible to deploy a control strategy, while being resilient to adversarial attacks. The core of our tool relies on the combination of convex programming with pseudo-Boolean satisfiability solving, following the lazy satisfiability modulo theory paradigm. We provide an empirical evaluation of the tool scalability, and demonstrate its application to attack detection and secure state estimation of electric power grids.