Secure state estimation for systems under mixed cyber-attacks: Security and performance analysis

Abstract

We study the state estimation for cyber-physical systems (CPSs) whose communication channels are subject to mixed denial-of-service (DoS) and false data injection (FDI) attacks. Cyber-attacks compromise the security and privacy of sensor and communication information. Unlike systems subject to only one single type of attacks (either DoS or FDI attacks), systems under mixed attacks will make the implementation of the optimal state estimation infeasible. We first obtain the optimal estimator for CPSs under mixed cyber-attacks. The optimal estimator consists of an exponentially growing number of components, and thus its computation effort exponentially grows in time. To efficiently compute the optimal estimate, we propose an approximate estimator by using the generalized pseudo-Bayesian algorithm. We prove that for a stable system, both the optimal estimator and the proposed approximate estimator are secure; and theoretically characterize the boundedness of the distance between the optimal and the approximate estimates. A simulation example is presented to illustrate the effectiveness of the proposed methods in guaranteeing secure state estimation when the privacy of sensor and communication information is at the risk of mixed cyber-attacks.