Efficient resilient dynamic co‐estimation framework for cyber‐physical systems under sensor attacks

Abstract

In this study, a novel co‐estimation approach is proposed for dynamic state estimation of cyber‐physical systems (CPSs) subjected to sensor attacks. In the proposed approach, the sensory measurements are preprocessed to extract some valuable information about the launched cyber‐attack. This information is then manipulated to form new state equations, which are augmented with the CPS model. The newly obtained model effectively represents the behaviour of both the CPS states as well as the launched cyber‐attack, and can be used for their co‐estimation. Two structures are suggested for the preprocessing of the sensory measurements that deploy Kalman filter (KF) and two‐step KF for co‐estimation of the states and cyber‐attacks. To effectively handle the concurrent effects of cyber‐attacks and unknown inputs on the CPS co‐estimation process, some auxiliary outputs are generated using high‐gain approximate differentiators to realise the required matching conditions. The proposed dynamic co‐estimation approach improves accuracy via considering the inter‐correlation between the CPS states and the cyber‐attacks. To demonstrate the viability of the proposed co‐estimation method, thorough stability and feasibility analysis are provided. Furthermore, extensive simulations are performed on a well‐known CPS‐the IEEE 14‐bus test system‐ to demonstrate the effectiveness of the proposed approach.

Centralized approximate optimal estimation for cyber‐physical systems under joint cyber‐attacks

“…𝛼 [i] k can be calculated by formula ( 13) and ( 14), with the CC of O G + O 2 . m [i] k and M [i] k are calculated by (12) with the CC of O KF . As at time k, there are N k p possible values, so the CC of the OE in Theorem 1 is…”

“…Next, the CC of the OE and AOE in Theorems 1 and 2 will be analyzed. For the convenience of describing, denote the cost of computing the Kalman filtering equations in (12), the Gaussian function…”

Distributed trust‐based unscented Kalman filter for non‐linear state estimation under cyber‐attacks: The application of manoeuvring target tracking over wireless sensor networks

“…For non-secure nodei, i ∈  NS , the goal is to classify n i neighbour nodes into two clusters based on the covariance matrix. The cluster centres are specified by p (1) i and p (2) i with random initial values. According to squared Euclidean distance between p + l (k) and the centres of clusters, the covariance…”

“…Recently, cyber-physical systems (CPSs) have received widespread attention in different fields of studies, such as industrial automation systems, transportation networks, smart grids, and wireless sensor networks (WSNs) [1,2]. WSNs have a wide range of applications, among which, target tracking is one of the most practical applications.…”

“…A diffusion-based distributed unscented Kalman filtering combined with a trust-based scheme is applied to ensure robustness against the cyber-attacks in manoeuvring target tracking applications over a wireless sensor network with secured nodes. Simulation results demonstrate the effectiveness of the proposed strategy in terms of tracking accuracy, while random attacks, false data injection attacks, and replay attacks are considered.Recently, cyber-physical systems (CPSs) have received widespread attention in different fields of studies, such as industrial automation systems, transportation networks, smart grids, and wireless sensor networks (WSNs) [1,2]. WSNs have a wide range of applications, among which, target tracking is one of the most practical applications.…”