On Redundant Observability: From Security Index to Attack Detection and Resilient State Estimation

Abstract

The security of control systems under sensor attacks is investigated. Redundant observability is introduced, explaining existing security notions including the security index, attack detectability, and observability under attacks. Equivalent conditions between redundant observability and existing notions are presented. Based on a bank of partial observers utilizing Kalman decomposition and a decoder exploiting redundancy, an estimator design algorithm is proposed enhancing the resilience of control systems. This scheme substantially improves computational efficiency utilizing far less memory.

Fully Distributed Resilient State Estimation Based on Distributed Median Solver

“…It is assumed that five agents are connected through the ring network, and κ = 0.5 and γ = 2 are used to construct (6). Measurement data injection attack is applied to the first sensor as a 1 (t) = π/3 for t ≥ 10.…”

State of the art of cyber-physical systems security: An automatic control perspective

“…We should also note that some of the aforementioned works are extensions of the research lines considered by our systematic mapping, since Bai et al From a modeling point of view, while Gaussian model of noise (used e.g. in Bai et al, 2017a;Chen et al, 2018b;Ding et al, 2017b;Ding et al, 2017a;Zheng et al, 2016;Mo and Sinopoli, 2016;Chen et al, 2017b;Kung et al, 2017;Mo and Garone, 2016;Bai et al, 2017b;Mishra et al, 2017;Murguia and Ruths, 2016;Li et al, 2017c;Li et al, 2017d;Shi et al, 2017;Forti et al, 2018;Ding et al, 2018b;Hu et al, 2016;Liu et al, 2016a;Wang et al, 2017 ) still clearly dominates the scene, the bounded model (found in Pajic et al, 2017b;Nakahira and Mo, 2018;Shoukry et al, 2018;Shoukry et al, 2017;Pajic et al, 2017a;Lee et al, 2018;Kim et al, 2018 ) is considered more and more often. This fact indicates an increasing attention to the aspects of robustness of the proposed solutions, and that the model-based methods and techniques for enforcing security in the cyber-physical domain are acquiring certain maturity.…”

“…In fact, also if we consider CPS dealing with cyber attacks with a generic dynamical systems modeling framework only, a huge amount of works can be found, as for example Bai et al, 2017a;Chen et al, 2018b;Pajic et al, 2017b;Ding et al, 2017b;2017a;Zheng et al, 2016;Yuan et al, 2016;Mo and Sinopoli, 2016;Chen et al, 2017b;Jin et al, 2017;Kung et al, 2017 ), just to cite a few. Another large amount of works can be found if we only focus our attention on attack detection and identification, and state estimation ( Nakahira and Mo, 2018;Mo and Garone, 2016;Weerakkody et al, 2017;Bai et al, 2017b;Mishra et al, 2017;Murguia and Ruths, 2016;Li et al, 2017c;2017d;Chen et al, 2017a;Shi et al, 2017;Shoukry et al, 2018;Pajic et al, 2017a;Shoukry and Tabuada, 2016;Ao et al, 2018;Lee et al, 2018;Forti et al, 2018;Kim et al, 2018 ). It is worth to emphasize that one of the path followed by researcher to improve the research in CPS security consists on considering more accurate, but also more complex, models such as stochastic, nonlinear and delayed systems ( Ding et al, 2018b;Hu et al, 2016;Liu et al, 2016a;Wang et al, 2017 ).…”

Observer Design for Cyber-Physical Systems With State Delay and Sparse Sensor Attacks

“…Based on the three inertia system constructed in [37], the following state-space equation is considered in this section.…”

“…The system (23) is evolved from the zero-order hold equivalent model of continuous-time state-space equation in [37], and the system parameters in this example are consistent with those in [37]. In addition, we set the sampling period as t = 0.05s, then the control input, the process noise and measurement noise are designed as u(k) = Kx(k), ψ(k) = 0.001 cos(πt)B and ϕ(k) = 0.001 sin(πt)B 1 respectively, where t t × k, K = [−1.9818, −0.2559, 1.6844, −0.0108, −0.1562, 0.0206] and B 1 = 1; 1; 1; 1; 1 .…”