arXiv subjects

Iñaki Esnaola

Publications and source records attributed to Iñaki Esnaola.

36 records · Page 2Linked to original sources

arXiv2023

Asymptotic Learning Requirements for Stealth Attacks on Linearized State Estimation

Information-theoretic stealth attacks are data injection attacks that minimize the amount of information acquired by the operator about the state variables, while simultaneously limiting the Kullback-Leibler divergence between the distribution of the measurements under attack and the distribution under normal operation with the aim of controling the probability of detection. For Gaussian distributed state variables, attack construction requires knowledge of the second order statistics of the state variables, which is estimated from a finite number of past realizations using a sample covariance matrix. Within this framework, the attack performance is studied for the attack construction with the sample covariance matrix. This results in an analysis of the amount of data required to learn the covariance matrix of the state variables used on the attack construction. The ergodic attack performance is characterized using asymptotic random matrix theory tools, and the variance of the attack performance is bounded. The ergodic performance and the variance bounds are assessed with simulations on IEEE test systems.

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arXiv2022

Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This generalization allows for a larger degree of flexibility in the incorporation of prior knowledge over the set of models. In this setting, the interplay of the regularization parameter, the reference measure, the risk function, and the empirical risk induced by the solution of the ERM-RER problem is characterized. This characterization yields necessary and sufficient conditions for the existence of a regularization parameter that achieves an arbitrarily small empirical risk with arbitrarily high probability. The sensitivity of the expected empirical risk to deviations from the solution of the ERM-RER problem is studied. The sensitivity is then used to provide upper and lower bounds on the expected empirical risk. Moreover, it is shown that the expectation of the sensitivity is upper bounded, up to a constant factor, by the square root of the lautum information between the models and the datasets.

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arXiv2022

An information theoretic vulnerability metric for data integrity attacks on smart grids

A novel metric that describes the vulnerability of the measurements in power systems to data integrity attacks is proposed. The new metric, coined vulnerability index (VuIx), leverages information theoretic measures to assess the attack effect on the fundamental limits of the disruption and detection tradeoff. The result of computing the VuIx of the measurements in the system yields an ordering of their vulnerability based on the level of exposure to data integrity attacks. This new framework is used to assess the measurement vulnerability of IEEE 9-bus and 30-bus test systems and it is observed that power injection measurements are overwhelmingly more vulnerable to data integrity attacks than power flow measurements. A detailed numerical evaluation of the VuIx values for IEEE test systems is provided.

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arXiv2022

Stealth Data Injection Attacks with Sparsity Constraints

Sparse stealth attack constructions that minimize the mutual information between the state variables and the observations are proposed. The attack construction is formulated as the design of a multivariate Gaussian distribution that aims to minimize the mutual information while limiting the Kullback-Leibler divergence between the distribution of the observations under attack and the distribution of the observations without attack. The sparsity constraint is incorporated as a support constraint of the attack distribution. Two heuristic greedy algorithms for the attack construction are proposed. The first algorithm assumes that the attack vector consists of independent entries, and therefore, requires no communication between different attacked locations. The second algorithm considers correlation between the attack vector entries which results in better attack performance at the expense of coordination between different locations. We numerically evaluate the performance of the proposed attack constructions on IEEE test systems and show that it is feasible to construct stealth attacks that generate significant disruption with a low number of compromised sensors.

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arXiv2022

Information Theoretic Data Injection Attacks with Sparsity Constraints

Information theoretic sparse attacks that minimize simultaneously the information obtained by the operator and the probability of detection are studied in a Bayesian state estimation setting. The attack construction is formulated as an optimization problem that aims to minimize the mutual information between the state variables and the observations while guaranteeing the stealth of the attack. Stealth is described in terms of the Kullback-Leibler (KL) divergence between the distributions of the observations under attack and without attack. To overcome the difficulty posed by the combinatorial nature of a sparse attack construction, the attack case in which only one sensor is compromised is analytically solved first. The insight generated in this case is then used to propose a greedy algorithm that constructs random sparse attacks. The performance of the proposed attack is evaluated in the IEEE 30 Bus Test Case.

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arXiv2022

Power Injection Measurements are more Vulnerable to Data Integrity Attacks than Power Flow Measurements

A novel metric that describes the vulnerability of the measurements in power system to data integrity attacks is proposed. The new metric, coined vulnerability index (VuIx), leverages information theoretic measures to assess the attack effect on the fundamental limits of the disruption and detection tradeoff. The result of computing the VuIx of the measurements in the system yields an ordering of the measurements vulnerability based on the level of exposure to data integrity attacks. This new framework is used to assess the measurements vulnerability of IEEE test systems and it is observed that power injection measurements are overwhelmingly more vulnerable to data integrity attacks than power flow measurements. A detailed numerical evaluation of the VuIx values for IEEE test systems is provided.

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arXiv2022

Covariance Estimation from Compressive Data Partitions using a Projected Gradient-based Algorithm

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing and communications applications, including denoising, spectrum sensing, and compression. Notice that estimating the covariance matrix from compressive samples leads to ill-posed minimizations with severe performance loss at high compression rates. In this regard, a regularization term is typically aggregated to the cost function to consider prior information about a particular property of the covariance matrix. Hence, this paper proposes an algorithm based on the projected gradient method to recover low-rank or Toeplitz approximations of the covariance matrix from compressive measurements. The algorithm divides the compressive measurements into data subsets projected onto different subspaces and accurately estimates the covariance matrix by solving a single optimization problem assuming that each data subset contains an approximation of the signal statistics. Furthermore, gradient filtering is included at every iteration of the proposed algorithm to minimize the estimation error. The error induced by the proposed splitting approach is analytically derived along with the convergence guarantees of the proposed method. The algorithm estimates the covariance matrix of hyperspectral images from synthetic and real compressive samples. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images from compressive measurements (8-15% approx). Moreover, simulations and theoretical results show that the filtering step reduces the recovery error up to twice the number of eigenvectors. Finally, an optical implementation is proposed, and real measurements are used to validate the theoretical findings.

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arXiv2021

Optimal Control over Multiple Input Lossy Channels

The performance of control systems with input packet losses on the controller to plant communication channel is analysed. The main contribution of this work is a proof that linear optimal control systems operating with UDP-like communication protocols have a larger quadratic cost than the same systems operating with TCP-like protocols. The proof is derived for the general case of multidimensional and independent actuation communication channels. In doing so, our results extend previous work to systems with multiple distributed actuators. The difference in cost between two communication protocols is analysed, enabling the maximal difference between the two protocols to be quantified. Numerical examples are presented to highlight the difference in costs induced by the choice of communication protocol.

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arXiv2021

Data-Injection Attacks

In this chapter we review some of the basic attack constructions that exploit a stochastic description of the state variables. We pose the state estimation problem in a Bayesian setting and cast the bad data detection procedure as a Bayesian hypothesis testing problem. This revised detection framework provides the benchmark for the attack detection problem that limits the achievable attack disruption. Indeed, the trade-off between the impact of the attack, in terms of disruption to the state estimator, and the probability of attack detection is analytically characterized within this Bayesian attack setting. We then generalize the attack construction by considering information-theoretic measures that place fundamental limits to a broad class of detection, estimation, and learning techniques. Because the attack constructions proposed in this chapter rely on the attacker having access to the statistical structure of the random process describing the state variables, we conclude by studying the impact of imperfect statistics on the attack performance. Specifically, we study the attack performance as a function of the size of the training data set that is available to the attacker to estimate the second-order statistics of the state variables.

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arXiv2020

Denial of Service Attacks on Control Systems with Packet Loss

The performance of control systems with packet loss as a result of an attack over the actuation communication channel is analysed. The operator is assumed to monitor the state of the channel by measuring the average number of packet losses and an attack detection criteria is established based on the statistic. The performance of the attacker is measured in terms of the increase of the linear quadratic cost function of the operator subject to a given detection constraint. Within that setting, the optimal denial of service (DoS) attack strategy is formulated for UDP-like and TCP-like communication protocols. {For both communication protocols,} DoS attack constructions that are independent and identically distributed (IID) are compared to those that are non-stationary. The main contributions of this paper are (i) explicit characterisation of the expected cost increase of the optimal attack constructions and the associated packet loss parameter for the IID case, (ii) proof, by example, that non-stationary random attacks outperform IID attacks in the presence of detection constraints.

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arXiv2020

Stealth Attacks on the Smart Grid

Random attacks that jointly minimize the amount of information acquired by the operator about the state of the grid and the probability of attack detection are presented. The attacks minimize the information acquired by the operator by minimizing the mutual information between the observations and the state variables describing the grid. Simultaneously, the attacker aims to minimize the probability of attack detection by minimizing the Kullback-Leibler (KL) divergence between the distribution when the attack is present and the distribution under normal operation. The resulting cost function is the weighted sum of the mutual information and the KL divergence mentioned above. The tradeoff between the probability of attack detection and the reduction of mutual information is governed by the weighting parameter on the KL divergence term in the cost function. The probability of attack detection is evaluated as a function of the weighting parameter. A sufficient condition on the weighting parameter is given for achieving an arbitrarily small probability of attack detection. The attack performance is numerically assessed on the IEEE 30-Bus and 118-Bus test systems.

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arXiv2019

Recovery of Missing Data in Correlated Smart Grid Datasets

We study the recovery of missing data from multiple smart grid datasets within a matrix completion framework. The datasets contain the electrical magnitudes required for monitoring and control of the electricity distribution system. Each dataset is described by a low rank matrix. Different datasets are correlated as a result of containing measurements of different physical magnitudes generated by the same distribution system. To assess the validity of matrix completion techniques in the recovery of missing data, we characterize the fundamental limits when two correlated datasets are jointly recovered. We then proceed to evaluate the performance of Singular Value Thresholding (SVT) and Bayesian SVT (BSVT) in this setting. We show that BSVT outperforms SVT by simulating the recovery for different correlated datasets. The performance of BSVT displays the tradeoff behaviour described by the fundamental limit, which suggests that BSVT exploits the correlation between the datasets in an efficient manner.

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arXiv2019

Universal Mutual Information Privacy Guarantees for Smart Meters

Smart meters enable improvements in electricity distribution system efficiency at some cost in customer privacy. Users with home batteries can mitigate this privacy loss by applying charging policies that mask their underlying energy use. A battery charging policy is proposed and shown to provide universal privacy guarantees subject to a constraint on energy cost. The guarantee bounds our strategy's maximal information leakage from the user to the utility provider under general stochastic models of user energy consumption. The policy construction adapts coding strategies for non-probabilistic permuting channels to this privacy problem.

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arXiv2019

Learning requirements for stealth attacks

The learning data requirements are analyzed for the construction of stealth attacks in state estimation. In particular, the training data set is used to compute a sample covariance matrix that results in a random matrix with a Wishart distribution. The ergodic attack performance is defined as the average attack performance obtained by taking the expectation with respect to the distribution of the training data set. The impact of the training data size on the ergodic attack performance is characterized by proposing an upper bound for the performance. Simulations on the IEEE 30-Bus test system show that the proposed bound is tight in practical settings.

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arXiv2018

Approximate Capacity Region of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback

In this paper, the capacity region of the linear deterministic interference channel with noisy channel-output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting; block-Markov superposition coding; and backward decoding. The proof of converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (GIC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits.

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arXiv2017

Robust Recovery of Missing Data in Electricity Distribution Systems

The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore, paramount. In this context, an algorithm for recovering missing state variable observations in electricity distribution systems is presented. The proposed method exploits the low rank structure of the state variables via a matrix completion approach while incorporating prior knowledge in the form of second order statistics. Specifically, the recovery method combines nuclear norm minimization with Bayesian estimation. The performance of the new algorithm is compared to the information-theoretic limits and tested trough simulations using real data of an urban low voltage distribution system. The impact of the prior knowledge is analyzed when a mismatched covariance is used and for a Markovian sampling that introduces structure in the observation pattern. Numerical results demonstrate that the proposed algorithm is robust and outperforms existing state of the art algorithms.

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arXiv2016

Approximate Capacity of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback

In this research report, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per channel use.

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arXiv2016

Approximate Capacity of the Gaussian Interference Channel with Noisy Channel-Output Feedback

In this paper, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per channel use.

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