In this paper, we study the impact of stealthy attacks on the Cyber-Physical System (CPS) modeled as a stochastic linear system. An attack is characterised by a malicious injection into the system through input, output or both, and it is called stealthy (resp. strictly stealthy) if it produces bounded changes (resp. no changes) in the detection residue. Correspondingly, a CPS is called vulnerable (resp. strictly vulnerable) if it can be destabilized by a stealthy attack (resp. strictly stealthy attack). We provide necessary and sufficient conditions for the vulnerability and strictly vulnerability. For the invulnerable case, we also provide a performance bound for the difference between healthy and attacked system. Numerical examples are provided to illustrate the theoretical results.

We study the problem of detecting an attack on a stochastic cyber-physical system. We aim to treat the problem in its most general form. We start by introducing the notion of asymptotically detectable attacks, as those attacks introducing changes to the system's output statistics which persist asymptotically. We then provide a necessary and sufficient condition for asymptotic detectability. This condition preserves generality as it holds under no restrictive assumption on the system and attacking scheme. To show the importance of this condition, we apply it to detect certain attacking schemes which are undetectable using simple statistics. Our necessary and sufficient condition naturally leads to an algorithm which gives a confidence level for attack detection. We present simulation results to illustrate the performance of this algorithm.

This article investigates the issue of distributed state estimation for a nonlinear hydraulic system. Our objective is to propose a distributed algorithm that enables individual nodes to obtain a global state estimation by utilizing local measurements and information gathered from neighboring nodes. We ensure global optimality by designing a mechanism for information exchange between neighboring nodes. The state estimation acquired by our distributed algorithm is equivalent to that of the centralized extended Kalman filter within a finite time. Our proposed algorithm is effective for acyclic network graphs and can be applied to cyclic network graphs through the loop removal approach. In addition, we provide a stability analysis of the proposed distributed algorithm. Finally, experiments on the practical platform are conducted to verify the feasibility and merits of the proposed algorithm.

This article focuses on the distributed static estimation problem. A belief propagation (BP) based estimation algorithm is studied for its convergence and accuracy. More precisely, we give conditions under which the BP-based distributed estimator is guaranteed to converge and we give concrete characterizations for its accuracy. Our results reveal new insights and properties of this distributed algorithm, leading to better theoretical understanding of static distributed state estimation and new applications of the algorithm.

Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on local measurements as well as information received from its neighbours. A recent algorithm has been proposed, which yields the optimal solution (i.e., the one that would be obtained using a centralized method) in finite time, provided the communication network forms an acyclic graph. If instead, the graph is cyclic, the only available alternative algorithm, which is based on iterative matrix inversion, achieving the optimal solution, does so asymptotically. However, it is also known that, in the cyclic case, the algorithm designed for acyclic graphs produces a solution which, although non optimal, is highly accurate. In this paper we do a theoretical study of the accuracy of this algorithm, in communication networks forming cyclic graphs. To this end, we provide bounds for the sub-optimality of the estimation error and the estimation error covariance, for a class of systems whose topological sparsity and signal-to-noise ratio satisfy certain condition. Our results show that, at each node, the accuracy improves exponentially with the so-called loop-free depth. Also, although the algorithm no longer converges in finite time in the case of cyclic graphs, simulation results show that the convergence is significantly faster than that of methods based on iterative matrix inversion. Our results suggest that, depending on the loop-free depth, the studied algorithm may be the preferred option even in applications with cyclic communication graphs.

In this paper, we study the impact of stealthy attacks on the Cyber-Physical System (CPS) modeled as a stochastic linear system. An attack is characterised by a malicious injection into the system through input, output or both, and it is called stealthy (resp.~strictly stealthy) if it produces bounded changes (resp.~no changes) in the detection residue. Correspondingly, a CPS is called vulnerable (resp.~strictly vulnerable) if it can be destabilized by a stealthy attack (resp.~strictly stealthy attack). We provide necessary and sufficient conditions for the vulnerability and strictly vulnerability. For the invulnerable case, we also provide a performance bound for the difference between healthy and attacked system. Numerical examples are provided to illustrate the theoretical results.