Secure State Estimation Problem Research Articles

Distributed Secure State Estimation and Control for CPSs Under Sensor Attacks.

In this paper, we investigate the distributed secure state estimation and control problems for interconnected cyber-physical systems (CPSs) with some sensors being attacked. First, by exploring the distinct properties of the unidentifiable attacks to a CPS, an explicit sufficient condition that the secure state estimation problem can be solvable is established. Then distributed preselectors and observers are presented to solve the secure state estimation problems. Furthermore, with the obtained state estimation, fractional dynamic surface-based distributed secure controllers are also proposed for the secure control problem. Theoretical analysis shows that, with the proposed distributed secure observers and controllers, not only the state of the CPS under attacks can be obtained in a given finite time but also the dynamic surface can be achieved and maintained in a finite time. Finally, the results are applied to an islanded micro-grid system as an illustration, which verifies the effectiveness of the proposed schemes.

Attack-Resilient <inline-formula> <tex-math notation="LaTeX">$\mathcal H_2$</tex-math> </inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\mathcal H_\infty$</tex-math> </inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\ell _1$</tex-math> </inline-formula> State Estimator

This paper considers the secure state estimation problem for noisy systems in the presence of sparse sensor integrity attacks. We show a fundamental limitation, that is, $2\rho$ -detectability is necessary for achieving bounded estimation errors, where $\rho$ is the number of attacks. This condition is weaker than the $2\rho$ -observability condition typically assumed in the literature. Conversely, we propose a real-time state estimator that achieves the fundamental limitation. The proposed state estimator is inspired by robust control and fault detection and isolation, that is, it consists of local Luenberger estimators, local residual detectors, and a global fusion process. We show its performance guarantees for $\mathcal H_2$ , $\mathcal H_\infty$ , and $\ell _1$ systems. Finally, numerical examples show that it has relatively low estimation errors among existing algorithms and average computation time for systems with a sufficiently small number of compromised sensors.

Secure Luenberger-like observers for cyber–physical systems under sparse actuator and sensor attacks

This paper investigates the secure state estimation problem for cyber–physical systems (CPSs) under sparse actuator and sensor attacks. By introducing the notion of orthogonal complement matrix, a necessary and sufficient condition for the state observability is provided. Then, based on the least square technique, a new projection operator is proposed to reconstruct the state from a set of successive measurements. Besides, by constructing an augmented system where the attacks are seen as part of the augmented state vector, a novel secure Luenberger-like observer is proposed, and sufficient conditions for the existence of the desired observer are proposed in terms of linear matrix inequalities (LMIs). It is shown that the proposed observability condition can be reduced to the sparse observability. A distinguishing point is that the attacks may be still unavailable even if the state is observable, and besides estimating the state, the attacks are also reconstructed by the proposed algorithm and observer according to their observability automatically.

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.

Secure state estimation for cyber-physical systems under sparse sensor attacks via a switched Luenberger observer

This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under disturbance and sparse sensor attacks. Both the fixed and switched target attacks are taken into account. Compared with the fixed target attacks, the switched target attacks, which are not considered in most existing results, change the attack targets at a limited frequency. The basic idea is designing a switched Luenberger observer for an augmented system where attacks are seen as part of its states. A new projection operator is proposed to ensure the sparsity of the attack estimations. Then, sufficient conditions for the existence of the desired switched observer are proposed in terms of linear matrix inequalities (LMIs) where the techniques for the switched systems with stable and unstable subsystems are introduced for tackling the switched target attacks. Compared with the existing results, no iterative algorithm is required here, and the proposed observer estimates the state well even under switched target attacks.