Optimal Innovation-Based Deception Attacks on Multi-Channel Cyber–Physical Systems

Optimal energy constrained deception attacks in cyber–physical systems with multiple channels: A fusion attack approach

Optimal deception attacks against remote state estimation in cyber-physical systems

Optimal stealthy false data injection attacks in cyber-physical systems

This study proposes the collaborative multiple attack strategy in cyber-physical systems (CPSs) under the energy constraint. Distinct from the relevant studies which only consider deception attacks or denial-of-service (DoS) attacks, the collaborative design of false data injection (FDI) attacks and DoS attacks is investigated, which is more general in the practical scenarios. The duration times for two types of attacks are limited due to the constraint of the attack energy. First, this work proposes an attack model which implements two types of attacks cooperatively. Then, under the proposed attack model, the attack performance is quantified by deriving the error covariance matrix, which is more intricate than the existing results since it involves more related terms that include the decision variables of the multiple attacks. Based on this, the attack design problem is converted into an optimisation problem with more constraints and decision variables. By analyzing the structure of the error covariance, it is proved that solving the optimisation problem is equivalent to step-wisely resolving the optimal distribution of FDI attacks and the optimal scheduling of multiple attacks without losing optimality. And then, the optimal distribution is obtained by utilising the Lagrange multiplier method, and the optimal scheduling is solved by 0-1 programming, such that the optimal attack strategy is obtained. Finally, the results are validated through the simulation examples.

Optimal linear attack for multi-sensor network against state estimation

This paper studies the optimal attack strategy for finite impulse response (FIR) systems identification with binary measurement under sequence replay attacks. First, the optimal attack strategy is formulated. In addition, methods for solving the optimal attack strategy under different conditions are provided. Second, a recursive algorithm is proposed to implement the attack strategy. Furthermore, the implementation of the optimal attack under various conditions is discussed. Finally, the feasibility of the proposed method is verified through numerical simulations.

The problem of stealthy innovation-based attacks in cyber-physical systems is studied in this paper. Different from the existing results which only utilize the current data, a more general attack strategy is designed by combining the historical and the current innovations to deteriorate the estimation performance and keep stealthy to the detector simultaneously. Under the framework of the attacks, the remote state estimation error is analyzed, and the optimal attack policy is derived by solving a convex optimization problem to achieve the maximal estimation error. Moreover, it is proved that the optimal attack strategy is piecewise constant, such that the attack is designed with low calculation cost. Finally, simulation examples are provided to demonstrate the theoretical results.

Optimal stealthy switching location attacks against remote estimation in cyber-physical systems

Single and double attacks are compared against a system consisting of identical parallel elements providing performance redundancy in a multi-state system. By destroying elements an attacker tries to maximize the expected damage caused by the reduction of the cumulative system performance. The attacker has a constrained resource which is distributed optimally between two attacks. The optimal number of attacked elements in each attack is determined. The attacker observes which elements are destroyed in the first attack and does not attack them in the second attack. First the optimal attack strategy against a system with a fixed number of elements is analysed. Thereafter a minmax two-period game between the attacker and the defender is considered. The defender distributes its constrained resource between deploying redundant elements and protecting them against the attack in the first period to minimize the expected damage. The attacker chooses its strategies in the second period to maximize the expected damage. A model and a methodology for finding the optimal defence and attack strategies are suggested. Illustrative examples of the optimal attack and defence are presented.

Optimal stealthy deception attack strategy under energy constraints

Optimal innovation-based deception attacks with side information against remote state estimation in cyber-physical systems

This paper proposes a new, affine-invariant image matching technique via accelerated KL (Kullback-Leibler) divergence minimization. First, we represent an image as a probability distribution by setting the sum of pixel values at one. Second, we introduce affine parameters into either of the two images' probability distributions using the Gaussian kernel density estimation. Finally, we determine optimal affine parameters that minimize KL divergence via an iterative method. In particular, without using such conventional nonlinear optimization techniques as the Levenberg-Marquardt method we devise an accelerated iterative method adapted to the KL divergence minimization problem through effective linear approximation. Recognition experiments using the handwritten numeral database IPTP CDROM1B show that the proposed method achieves a much higher recognition rate of 91.5% at suppressed computational cost than that of 83.7% obtained by a simple image matching method based on a normal KL divergence.

Waveform design for target identification and classification in multiple-input multiple-output (MIMO) radar systems has been studied in several recent works. In previous works, optimal signals for an estimation algorithm are found assuming that only signal- independent noise exists. This work extends previous research by studying the case where clutter is also present. We develop a procedure to design the optimal waveform which minimizes estimation error at the output of the minimum mean squared error (MMSE) estimators in two scenarios. In the first one different transmit antennas see uncorrelated aspects of the target, and we consider the correlated target aspects in the second one. Estimation error in the first case will not zero even if the transmit power tends to infinity. This value of this error is referred to as the lower estimation error bound ε <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OUND</i> . It can be shown that since the MIMO radar receiver can null out the clutter subspace, ε <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OUND</i> is zero in the second scenario. Waveform design for MMSE estimator under the uncorrelated target aspects assumption, leads to the semi-definite programming (SDP) problem, a convex optimization problem which can be efficiently solved through numerical methods. An explicit solution is developed for this SDP problem in two cases. In the first case target and clutter covariance matrices are jointly diagonalizable, and in the second one the signal-to-noise ratio (SNR) is sufficiently high. Finding optimal transmit signals for the correlated target aspects scenario also results in an SDP problem.

The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the standard Gaussian distribution is usually used for the prior, this simple prior incurs over-regularization. As a sophisticated prior, the aggregated posterior has been introduced, which is the expectation of the posterior over the data distribution. This prior is optimal for the VAE in terms of maximizing the training objective function. However, KL divergence with the aggregated posterior cannot be calculated in a closed form, which prevents us from using this optimal prior. With the proposed method, we introduce the density ratio trick to estimate this KL divergence without modeling the aggregated posterior explicitly. Since the density ratio trick does not work well in high dimensions, we rewrite this KL divergence that contains the high-dimensional density ratio into the sum of the analytically calculable term and the lowdimensional density ratio term, to which the density ratio trick is applied. Experiments on various datasets show that the VAE with this implicit optimal prior achieves high density estimation performance.

In an urban setting, sound levels vary over time and space due to transportation, construction, and other community noise sources. Parametric probability density functions (PDFs) can concisely characterize these variations, but the literature does not identify an appropriate PDF that both has a firm theoretical foundation and fits urban sound data well. A Gaussian distribution, which physically corresponds to a single dominant source, sometimes describes a distribution of levels well, but often it does not. Frequently, the distribution falls somewhere between the idealizations of a single dominant source and many comparable sources, so a model that can approximate both cases could perform better than a Gaussian distribution. To that end, this presentation considers the generalized gamma and compound gamma distributions for modeling the normalized mean squared pressure. Creating histograms of acoustic data, which were collected in Boston, provides a basis to compare the distributions using the Kullback-Leibler (KL) divergence. In general, compared to the generalized gamma and log-normal distributions, the compound gamma distribution has a lower KL divergence and thus more closely matches the experimental distributions.