We present an analysis of a heuristic for abrupt change detection of systems with bounded state variations. The proposed analysis is based on the Singular Value Decomposition (SVD) of a history matrix built from system observations. We show that monitoring the largest singular value of the history matrix can be used as a heuristic for detecting abrupt changes in the system outputs. We provide sufficient detectability conditions for the proposed heuristic. As an application, we consider detecting malicious cyber data attacks on power systems and test our proposed heuristic on the IEEE 39-bus testbed.
@cite_16: The problem of detecting and characterizing impacts of malicious attacks against smart grid state estimation is considered. Different from the classical bad data detection for state estimation, the detection of malicious data injected by an adversary must take into account carefully designed attacks capable of evading conventional bad data detection. A Bayesian framework is presented for the characterization of fundamental tradeoffs at the control center and for the adversary. For the control center, a detector based on the generalized likelihood ratio test (GRLT) is introduced and compared with conventional bad detection detection schemes. For the adversary, the tradeoff between increasing the mean square error (MSE) of the state estimation vs. the probability of being detected by the control center is characterized. A heuristic is presented for the design of worst attack.
@cite_4: We consider the problem of state-estimation of a linear dynamical system when some of the sensor measurements are corrupted by an adversarial attacker. The errors injected by the attacker in the sensor measurements can be arbitrary and are not assumed to follow a specific model (in particular they can be of arbitrary magnitude). We first characterize the number of attacked sensors that can be tolerated so that the state of the system can still be correctly recovered by any decoding algorithm. We then propose a specific computationally feasible decoding algorithm and we give a characterization of the number of errors this decoder can correct. For this we use ideas from compressed sensing and error correction over the reals and we exploit the dynamical nature of the problem. We show using numerical simulations that this decoder performs very well in practice and allows to correct a large number of errors.
@cite_16 assume a Bayesian model on the state variables and consider a binary detection problem. In particular, they assume that the state variables have a zero-mean Gaussian distribution. @cite_4 impose a linear state-space representation on the power system state evolution and propose a decoder that corrects for the compromised meters. In their plant model, they assume they know the state transition and measurement matrices.