Risk-based Security Measure Allocation Against Injection Attacks on Actuators

This article considers the problem of risk-optimal allocation of security measures when the actuators of an uncertain control system are under attack. We consider an adversary injecting false data into the actuator channels. The attack impact is characterized by the maximum performance loss caused by a stealthy adversary with bounded energy. Since the impact is a random variable, due to system uncertainty, we use Conditional Value-at-Risk (CVaR) to characterize the risk associated with the attack. We then consider the problem of allocating the security measures which minimize the risk. We assume that there are only a limited number of security measures available. Under this constraint, we observe that the allocation problem is a mixed-integer optimization problem. Thus we use relaxation techniques to approximate the security allocation problem into a Semi-Definite Program (SDP). We also compare our allocation method $(i)$ across different risk measures: the worst-case measure, the average (nominal) measure, and $(ii)$ across different search algorithms: the exhaustive and the greedy search algorithms. We depict the efficacy of our approach through numerical examples.Comment: Submitted to IEEE Open Journal of Control Systems (OJ-CSYS

Risk Assessment of Stealthy Attacks on Uncertain Control Systems

In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering data injection attacks that aim at maximizing impact while remaining undetected, we use the recently proposed output-to-output gain to characterize the risk associated with the impact of attacks under a limited system knowledge attacker. The risk is formulated using a well-established risk metric, namely the maximum expected loss. Under this setups, the risk assessment problem corresponds to an untractable infinite non-convex optimization problem. To address this limitation, we adopt the framework of scenario-based optimization to approximate the infinite non-convex optimization problem by a sampled non-convex optimization problem. Then, based on the framework of dissipative system theory and S-procedure, the sampled non-convex risk assessment problem is formulated as an equivalent convex semi-definite program. Additionally, we derive the necessary and sufficient conditions for the risk to be bounded. Finally, we illustrate the results through numerical simulation of a hydro-turbine power system

A Zero-Sum Game Framework for Optimal Sensor Placement in Uncertain Networked Control Systems under Cyber-Attacks

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious adversary and a detector. Given a protected performance vertex, we consider a detector, with uncertain system knowledge, that selects another vertex on which to place a sensor and monitors its output with the aim of detecting the presence of the adversary. On the other hand, the adversary, also with uncertain system knowledge, chooses a single vertex and conducts a cyber-attack on its input. The purpose of the adversary is to drive the attack vertex as to maximally disrupt the protected performance vertex while remaining undetected by the detector. As our first contribution, the game payoff of the above-defined zero-sum game is formulated in terms of the Value-at-Risk of the adversary's impact. However, this game payoff corresponds to an intractable optimization problem. To tackle the problem, we adopt the scenario approach to approximately compute the game payoff. Then, the optimal monitor selection is determined by analyzing the equilibrium of the zero-sum game. The proposed approach is illustrated via a numerical example of a 10-vertex networked control system.Comment: 8 pages, 3 figues, Accepted to the 61st Conference on Decision and Control, Cancun, December 202

Design of multiplicative watermarking against covert attacks

This paper addresses the design of an active cyberattack detection architecture based on multiplicative watermarking, allowing for detection of covert attacks. We propose an optimal design problem, relying on the so-called output-to-output l2-gain, which characterizes the maximum gain between the residual output of a detection scheme and some performance output. Although optimal, this control problem is non-convex. Hence, we propose an algorithm to design the watermarking filters by solving the problem suboptimally via LMIs. We show that, against covert attacks, the output-to-output l2-gain is unbounded without watermarking, and we provide a sufficient condition for boundedness in the presence of watermarks.Comment: 6 page conference paper accepted to the 60th IEEE Conference on Decision and Contro

Risk-averse controller design against data injection attacks on actuators for uncertain control systems

In this paper, we consider the optimal controller design problem against data injection attacks on actuators for an uncertain control system. We consider attacks that aim at maximizing the attack impact while remaining stealthy in the finite horizon. To this end, we use the Conditional Value-at-Risk to characterize the risk associated with the impact of attacks. The worst-case attack impact is characterized using the recently proposed output-to-output $\ell_2$-gain (OOG). We formulate the design problem and observe that it is non-convex and hard to solve. Using the framework of scenario-based optimization and a convex proxy for the OOG, we propose a convex optimization problem that approximately solves the design problem with probabilistic certificates. Finally, we illustrate the results through a numerical example.Comment: Accepted for publication to the 2022 American Control Conferenc

Joint controller and detector design against data injection attacks on actuators

This paper addresses the issue of data injection attacks on actuators in control systems. Considering attacks that aim at maximizing impact while remaining undetected, the paper revisits the recently proposed output-to-output gain, which is compared to classical sensitivity metrics such as H-infinity and H_. In its original formulation, the output-to-output gain is unbounded for strictly proper systems. This limitation is further investigated and addressed by modifying the performance output of the system and ensuring that the system from attack signal to performance output is also strictly proper. With this system description, and by using the theory of dissipative systems, a Bi-linear Matrix Inequality (BMI) is formulated for system design. Using this BMI, a design algorithm is proposed based on the heuristic of alternating minimization. Through numerical simulations of the proposed algorithm, it is found that the output-to-output gain presents advantages over the other metrics: the effect of the attack is reduced in the performance output and increased in the detection output in a relatively large spectrum of frequencies

Microstructural, phase evolution and corrosion properties of silicon carbide reinforced pulse electrodeposited nickel-tungsten composite coatings

Silicon carbide (SiC) reinforced nickel-tungsten (Ni-W) coatings were successfully fabricated on steel substrate by pulse electrodeposition method (PED) and the amount of SiC was varied as 0 g/l, 2 g/l, and 5 g/l in Ni-W coating. Effect of subsequent addition of SiC on microstructures, phases and on corrosion property of the coating was investigated. Field emission scanning electron microscopy (FE-SEM) image of the surface morphology of the coating showed the transformation from the dome like structure to turtle shell like structure. X-ray diffraction (XRD) of Ni-W-5 g/l SiC showed the disappearance of (220) plane of Ni(W), peak splitting in major peak of Ni(W) and formation of distinct peak of W(Ni) solid solution. Absence of (220) plane, peak splitting and presence of W(Ni) solid solution was explained by the high resolution transmission electron microscopy (HR-TEM) images. Tafel polarization plot was used to study the corrosion property of the coatings in 0.5 M NaCl solution. Ni-W-5 g/l SiC coating was showed higher corrosion resistance (i.e. similar to 21% increase in corrosion potential, E-corr) compared to Ni-W coating. Two simultaneous phenomena have been identified for the enhanced corrosion resistance of Ni-W-5 g/l SiC coating. (a) Presence of crystallographic texture (b) formation of continuous double barrier layer of NiWO4 and SiO2. (C) 2015 Elsevier B.V. All rights reserved