We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher’s equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher’s equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

Adversarial patches are capable of misleading computer vision systems based on convolutional neural networks. Existing recovery methods suffer of at least one of three fundamental shortcomings: no information about the presence of patches in the scene, inability to efficiently handle noncontiguous patch attacks, and a strong reliance on fixed saliency thresholds. We propose Saliuitl, a recovery method independent of the number of patches and their shape, which unlike prior works, explicitly detects patch attacks before attempting recovery. In our approach, detection is based on the attributes of a binarized feature map ensemble, which is generated by using an ensemble of saliency thresholds. If an attack is detected, Saliuitl recovers clean predictions locating patches guided by an ensemble of binarized feature maps and inpainting them. We evaluate Saliuitl on widely used object detection and image classification benchmarks from the adversarial patch literature, and our results show that compared to recent state-of-the-art defenses, Saliuitl achieves a recovery rate up to 97.81 and 42.63 percentage points higher at the same rate of lost predictions for image classification and object detection, respectively. By design, Saliuitl has low computational complexity and is robust to adaptive white-box attacks. Our code is available at https://github.com/Saliuitl/Saliuitl/tree/main.

In this article, we study the voltage regulation problem for an inverter-interfaced power distribution network that is subject to possible adversarial injections and/or severe fault scenarios. Different from the current literature, our aim is not just to regulate the voltage levels on the gridline within the prescribed range, but also to provide a measure of reliability for the safe operation of the grid with respect to such adversarial events. In that respect, we propose the framework of resilient control design which ensures safe operation of the grid under nominal conditions (with regard to the given voltage regulation objective) and, additionally, offers theoretical guarantees of finite-time recovery following intermittent fault/ safety violations. To validate these claims, we test the proposed resilient controller on a dedicated testbed for power inverter networks and, through hardware-in-the-loop (HIL) simulation case studies, showcase the efficacy of the suggested control scheme.

Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected $l^2$-distance bounds between the LSE and the true regression function, where expectation is evaluated on a fresh, counterfactual, trajectory. We leverage recently developed information-theoretic methods to establish the optimality of the LSE for nonparametric hypotheses classes in terms of supremum norm metric entropy and a subgaussian parameter. Next, we relate this subgaussian parameter to the stability of the underlying process using notions from dynamical systems theory. When combined, these developments lead to rate-optimal error bounds that scale as $T^{-1/(2+q)}$ for suitably stable processes and hypothesis classes with metric entropy growth of order $\delta^{-q}$. Here, $T$ is the length of the observed trajectory, $\delta \in \mathbb{R}_+$ is the packing granularity and $q\in (0,2)$ is a complexity term. Finally, we specialize our results to a number of scenarios of practical interest, such as Lipschitz dynamics, generalized linear models, and dynamics described by functions in certain classes of Reproducing Kernel Hilbert Spaces (RKHS).

In this paper, we develop a framework against inference attacks aimed at inferring the values of the controller gains of an active steering control system (ASCS). We first show that an adversary with access to the shared information by a vehicle, via a vehicular ad hoc network (VANET), can reliably infer the values of the controller gains of an ASCS. This vulnerability may expose the driver as well as the manufacturer of the ASCS to severe financial and safety risks. To protect controller gains of an ASCS against inference attacks, we propose a randomized filtering framework wherein the lateral velocity and yaw rate states of a vehicle are processed by a filter consisting of two components: a nonlinear mapping and a randomizer. The randomizer randomly generates a pair of pseudo gains which are different from the true gains of the ASCS. The nonlinear mapping performs a nonlinear transformation on the lateral velocity and yaw rate states. The nonlinear transformation is in the form of a dynamical system with a feedforward-feedback structure which allows real-time and causal implementation of the proposed privacy filter. The output of the filter is then shared via the VANET. The optimal design of randomizer is studied under a privacy constraint that determines the protection level of controller gains against inference attacks, and is in terms of mutual information. It is shown that the optimal randomizer is the solution of a convex optimization problem. By characterizing the distribution of the output of the filter, it is shown that the statistical distribution of the filter’s output depends on the pseudo gains rather than the true gains. Using information-theoretic inequalities, we analyze the inference ability of an adversary in estimating the control gains based on the output of the filter. Our analysis shows that the performance of any estimator in recovering the controller gains of an ASCS based on the output of the filter is limited by the privacy constraint. The performance of the proposed privacy filter is compared with that of an additive noise privacy mechanism. Our numerical results show that the proposed privacy filter significantly outperforms the additive noise mechanism, especially in the low distortion regime.

5G and beyond 5G low power wireless networks make Internet of Things (IoT) and Cyber-Physical Systems (CPS) applications capable of serving massive amounts of devices and machines. Due to the broadcast nature of wireless networks, it is crucial to secure the communication between these devices and machines from spoofing and interception attacks. This paper is concerned with the security of carrier frequency offset (CFO) based continuous physical layer authentication. The interaction between an attacker and a defender is modeled as a dynamic discrete leader-follower game with imperfect information. In the considered model, a legitimate user (Alice) communicates with the defender/operator (Bob) and is authorized by her CFO continuously. The attacker (Eve), by listening/eavesdropping the communication between Alice and Bob, tries to learn the CFO characteristics of Alice and aims to inject malicious packets to Bob by impersonating Alice. First, by showing that the optimal attacker strategy is a threshold policy, an optimization problem of the attacker with exponentially growing action space is reduced to a tractable integer optimization problem with a single parameter, then the corresponding defender cost is derived. Extensive simulations illustrate the characteristics of optimal strategies/utilities of the players depending on the actions, and show that the defender’s optimal false positive rate causes attack success probabilities to be in the order of 0.99. The results show the importance of the parameters while finding the balance between system security and efficiency.

Most existing industrial control systems (ICSs), such as building energy management systems (EMSs), were installed when potential security threats were only physical. With advances in connectivity, ICSs are now, typically, connected to communications networks and, as a result, can be accessed remotely. This extends the attack surface to include the potential for sophisticated cyber attacks, which can adversely impact ICS operation, resulting in service interruption, equipment damage, safety concerns, and associated financial implications. In this work, a novel cyber-physical security framework for ICSs is proposed, which incorporates an analytics tool for attack detection and executes a reliable estimation-based attack-resilient control policy, whenever an attack is detected. The proposed framework is adaptable to already implemented ICS and the stability and optimal performance of the controlled system under attack has been proved. The performance of the proposed framework is evaluated using a reduced order model of a real EMS site and simulated attacks.

While attacks on information systems have for most practical purposes binary outcomes (information was manipulated/eavesdropped, or not), attacks manipulating the sensor or control signals of Industrial Control Systems (ICS) can be tuned by the attacker to cause a continuous spectrum in damages. Attackers that want to remain undetected can attempt to hide their manipulation of the system by following closely the expected behavior of the system, while injecting just enough false information at each time step to achieve their goals. In this work, we study if attack-detection can limit the impact of such stealthy attacks. We start with a comprehensive review of related work on attack detection schemes in the security and control systems community. We then show that many of those works use detection schemes that are not limiting the impact of stealthy attacks. We propose a new metric to measure the impact of stealthy attacks and how they relate to our selection on an upper bound on false alarms. We finally show that the impact of such attacks can be mitigated in several cases by the proper combination and configuration of detection schemes. We demonstrate the effectiveness of our algorithms through simulations and experiments using real ICS testbeds and real ICS systems.

In this paper, we consider a discrete time linear quadratic Gaussian (LQG) control problem in which state information of the plant is encoded in a variable-length binary codeword at every time step, and a control input is determined based on the codewords generated in the past. We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance. This lower bound coincides with the infimum of a certain directed information expression, and is computable by semidefinite programming (SDP). Based on a technique by Silva et al., we also provide an upper bound of the best achievable rate by constructing a controller equipped with a uniform quantizer with subtractive dither and Shannon-Fano coding. The gap between the obtained lower and upper bounds is less than 0:754r + 1 bits per time step regardless of the required LQG control performance, where r is the rank of a signal-to-noise ratio matrix obtained by SDP, which is no greater than the dimension of the state.

The zero-error secrecy capacity of uncertain wiretap channels is defined. If the sensor-estimator channel is perfect, it is also calculated. Further properties are discussed. The problem of estimating a dynamical system with nonstochastic disturbances is studied where the sensor is connected to the estimator and an eavesdropper via an uncertain wiretap channel. The estimator should obtain a uniformly bounded estimation error whereas the eavesdropper's error should tend to infinity. It is proved that the system can be estimated securely if the zero-error capacity of the sensor-estimator channel is strictly larger than the logarithm of the system's unstable pole and the zero-error secrecy capacity of the uncertain wiretap channel is positive.

In this paper, we propose a robust approach for scheduling of smart appliances and electrical energy storages (EESs) in active apartments with the aim of reducing both the electricity bill and the CO2emissions. The proposed robust formulation takes the user behavior uncertainty into account so that the optimal appliances schedule is less sensitive to unpredictable changes in user preferences. The user behavior uncertainty is modeled as uncertainty in the cost function coefficients. In order to reduce the level of conservativeness of the robust solution, we introduce a parameter allowing to achieve a trade-off between the price of robustness and the protection against uncertainty. Mathematically, the robust scheduling problem is posed as a multi-objective Mixed Integer Linear Programming (MILP), which is solved by using standard algorithms. The numerical results show effectiveness of the proposed approach to increase both the electricity bill and CO2emissions savings, in the presence of user behavior uncertainties. Mathematical insights into the robust formulation are illustrated and the sensitivity of the optimum cost in the presence of uncertainties is investigated. Although home appliances and EESs are considered in this work, we point out that the proposed scheduling framework is generally applicable to many use cases, e.g., charging and discharging of electrical vehicles in an effective way. In addition, it is applicable to various scenarios considering different uncertainty sources, different storage technologies and generic programmable electrical loads, as well as different optimization criteria.

In this paper, we study the impact of adversarial actions on voltage control schemes in interconnected microgrids. Each microgrid is abstracted as a power inverter that can be controlled to regulate its voltage magnitude and phase-angle independently. Moreover, each power inverter is modeled as a single integrator, whose input is given by a voltage droop-control policy that is computed based on voltage magnitude and reactive power injection measurements. Under mild assumptions, we then establish important properties of the nominal linearized closed-loop system, such as stability, positivity, and diagonal dominance. These properties play an important role when characterizing the potential impact of different attack scenarios. In particular, we discuss two attack scenarios where the adversary corrupts measurement data and reference signals received by the voltage droop controllers. The potential impact of instances of each scenario is analyzed using control-theoretic tools, which may be used to develop methodologies for identifying high-risk attack scenarios, as is illustrated by numerical examples.

We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgment rates and delays are mathematically modeled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packet-level simulations demonstrate the accuracy of the proposed model.

The ability to maintain state awareness in the face of unexpected and unmodeled errors and threats is a defining feature of a resilient control system. Therefore, in this paper, we study the problem of distributed fault detection and isolation (FDI) in large networked systems with uncertain system models. The linear networked system is composed of interconnected subsystems and may be represented as a graph. The subsystems are represented by nodes, while the edges correspond to the interconnections between subsystems. Considering faults that may occur on the interconnections and subsystems, as our first contribution, we propose a distributed scheme to jointly detect and isolate faults occurring in nodes and edges of the system. As our second contribution, we analyze the behavior of the proposed scheme under model uncertainties caused by the addition or removal of edges. Additionally, we propose a novel distributed FDI scheme based on local models and measurements that is resilient to changes outside of the local subsystem and achieves FDI. Our third contribution addresses the complexity reduction of the distributed FDI method, by characterizing the minimum amount of model information and measurements needed to achieve FDI and by reducing the number of monitoring nodes. The proposed methods can be fused to design a scalable and resilient distributed FDI architecture that achieves local FDI despite unknown changes outside the local subsystem. The proposed approach is illustrated by numerical experiments on the IEEE 118-bus power network benchmark.

Critical power system applications like contingency analysis and optimal power flow calculation rely on the power system state estimator. Hence the security of the state estimator is essential for the proper operation of the power system. In the future more applications are expected to rely on it, so that its importance will increase. Based on realistic models of the communication infrastructure used to deliver measurement data from the substations to the state estimator, in this paper we investigate the vulnerability of the power system state estimator to attacks performed against the communication infrastructure. We define security metrics that quantify the importance of individual substations and the cost of attacking individual measurements. We propose approximations of these metrics, that are based on the communication network topology only, and we compare them to the exact metrics. We provide efficient algorithms to calculate the security metrics. We use the metrics to show how various network layer and application layer mitigation strategies, like single and multi-path routing and data authentication, can be used to decrease the vulnerability of the state estimator. We illustrate the efficiency of the algorithms on the IEEE 118 and 300 bus benchmark power systems.

In this letter, we study the problem of fault detection and mitigation in networks where the measurements satisfy Kirchhoff's voltage law. First, we characterise the class of faults appearing as an additive fault vector (injected by a malicious adversary or due to equipment failures) that can be detected by taking into account the topology of the network. Second, we consider the problem of estimating the fault vector via tools from compressive sensing. Moreover, we comment on the applicability of the developed methods to the case where the measurements satisfy Kirchhoff's current law. The proposed methods are validated via numerical examples with application to time synchronization networks.