Secure state estimation and control using multiple (insecure) observers

Motivated by the need to protect Cyber-Physical Systems against attacks, we consider in this paper the problem of estimating the state in a private and secure manner despite active adversary attacks; adversaries that can attack the software/ hardware where state estimation is performed. To combat such threats, we propose an architecture where state estimation is performed across multiple computing nodes (observers). We then show that even when ρ out of a total 3ρ +1 observers are actively attacked: 1) using a combination of outputs from the observers, the state is still correctly estimated; 2) the physical plant is still correctly controlled; 3) the adversary can only obtain limited knowledge about the state. Our approach is inspired by techniques in cryptography for secure message transmission and information-theoretic secrecy. In addition, our guarantees on the secrecy of the plant´s state against corrupting observers are based on the Cramer-Rao lower bound from estimation theory.