Finite time attack detection and supervised secure state estimation for CPSs with malicious adversaries

In this paper, we investigate the finite time attack detection and secure state estimation problem for linear cyber physical systems (CPS) with s out of p sensors being attacked. By exploring the distinct properties of the undetectable and indistinguishable attacks to a CPS, novel explicit criteria on the detectability and distinguishability of the CPS under attack are proposed in terms of the r-resilient observability. This enables us to explicitly characterize the undetectable and/or indistinguishable attacks to the CPS. Then based on such characterization, we propose a finite time detector to solve the attack detection problem and a finite time alarm event driven supervised estimator to solve the secure state estimation problem, separately. Theoretical analysis shows that, the proposed detector and estimator can detect attacks and estimate the state within a prescribed finite time, respectively. Finally, some numerical simulations on an unmanned ground vehicle as an illustration of attack detection and secure state estimation is proposed to verify the effectiveness of the proposed schemes.