No Arabic abstract
This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are $mathtt{M}$ independent systems, each of which has a remote sensor monitoring the system and sending its local estimates to a fusion center over a packet-dropping channel. An attacker may generate noises to exacerbate the communication channels between sensors and the fusion center. Due to capacity limitation, at each time the attacker can exacerbate at most $mathtt{N}$ of the $mathtt{M}$ channels. The goal of the attacker side is to seek an optimal policy maximizing the estimation error at the fusion center. The problem is formulated as a Markov decision process (MDP) problem, and the existence of an optimal deterministic and stationary policy is proved. We further show that the optimal policy has a threshold structure, by which the computational complexity is reduced significantly. Based on the threshold structure, a myopic policy is proposed for homogeneous models and its optimality is established. To overcome the curse of dimensionality of MDP algorithms for general heterogeneous models, we further provide an asymptotically (as $mathtt{M}$ and $mathtt{N}$ go to infinity) optimal solution, which is easy to compute and implement. Numerical examples are given to illustrate the main results.
We consider a class of malicious attacks against remote state estimation. A sensor with limited resources adopts an acknowledgement (ACK)-based online power schedule to improve the remote state estimation performance. A malicious attacker can modify the ACKs from the remote estimator and convey fake information to the sensor. When the capability of the attacker is limited, we propose an attack strategy for the attacker and analyze the corresponding effect on the estimation performance. The possible responses of the sensor are studied and a condition for the sensor to discard ACKs and switch from online schedule to offline schedule is provided.
An unobservable false data injection (FDI) attack on AC state estimation (SE) is introduced and its consequences on the physical system are studied. With a focus on understanding the physical consequences of FDI attacks, a bi-level optimization problem is introduced whose objective is to maximize the physical line flows subsequent to an FDI attack on DC SE. The maximization is subject to constraints on both attacker resources (size of attack) and attack detection (limiting load shifts) as well as those required by DC optimal power flow (OPF) following SE. The resulting attacks are tested on a more realistic non-linear system model using AC state estimation and ACOPF, and it is shown that, with an appropriately chosen sub-network, the attacker can overload transmission lines with moderate shifts of load.
We address the problem of state estimation, attack isolation, and control for discrete-time Linear Time Invariant (LTI) systems under (potentially unbounded) actuator false data injection attacks. Using a bank of Unknown Input Observers (UIOs), each observer leading to an exponentially stable estimation error in the attack-free case, we propose an estimator that provides exponential estimates of the system state and the attack signals when a sufficiently small number of actuators are attacked. We use these estimates to control the system and isolate actuator attacks. Simulations results are presented to illustrate the performance of the results.
This paper studies remote state estimation in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, while an eavesdropper can successfully overhear each sensor transmission with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behaviour in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded. An alternative measure of security, constraining the amount of information revealed to the eavesdropper, is also considered, and similar structural results on the optimal transmission policy are derived. In the infinite horizon situation with unstable systems, it is now shown that for any transmission policy which keeps the expected estimation error covariance bounded, the expected amount of information revealed to the eavesdropper is always lower bounded away from zero. An extension of our results to the transmission of measurements is also presented.
Jointly optimal transmission power control and remote estimation over an infinite horizon is studied. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogeneous Markov chain. The successful transmission probability depends on both the channel gains and the transmission power used by the sensor. The transmission power control rule and the remote estimator should be jointly designed, aiming to minimize an infinite-horizon cost consisting of the power usage and the remote estimation error. A first question one may ask is: Does this joint optimization problem have a solution? We formulate the joint optimization problem as an average cost belief-state Markov decision process and answer the question by proving that there exists an optimal deterministic and stationary policy. We then show that when the monitored dynamic process is scalar, the optimal remote estimates depend only on the most recently received sensor observation, and the optimal transmission power is symmetric and monotonically increasing with respect to the innovation error.