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  • 1.
    Milosevic, Jezdimir
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Model Based Impact Analysis and Security Measure Allocation for Control Systems2018Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Improvement of cyber-security of industrial control systems is of utmost importance for our society. It has been recognized that many security vulnerabilities can be found in these systems, which if exploited may lead to dire consequences. For instance, successful cyber-attacks against industrial control systems may cause loss of electricity, lead to shortage of drinkable water,or disrupt oil and gas production. Deploying security measures to protect industrial control systems may be costly.  Thus, it is expected that we would not be able to prevent all the security vulnerabilities that we find within the systems. In this thesis, we consider two problems related to this issue. The first one is how to determine which combinations of vulnerabilities are the most critical to be prevented. An important part of this classification is estimating the impact of cyber-attacks conducted using these vulnerabilities, which is the first major problem considered in the thesis. The budget for deploying security measures can then be focused on preventing the most critical combinations of vulnerabilities that are found. How to do this in an optimal way once the number of vulnerabilities and measures is large is the second major problem considered. As our first contribution, we outline a framework for estimating the attack impact in industrial control systems. Here, we consider industrial control systems that have both control and monitoring tasks. For industrial control systems with control tasks, we propose a framework to estimate the impact of several attack strategies. We prove that the estimation of the impact of all possible strategies is reducible to solving a set of convex minimization problems. The solvers for convex minimization problems are well known, so the exact value of the attack impact can be obtained easily. For industrial control systems with monitoring tasks, we analyze the impact of a bias injection attack strategy.  We prove that the attack impact can be obtained as the solution of a quadratically constrained quadratic program, for which the exact solution can be found efficiently. We also introduce a lower bound of the attack impact in terms of the number of compromised sensors. The theoretical findings are illustrated in numerical examples. As our second contribution, we propose a flexible modeling framework for allocating security measures. Our framework is suitable for dynamical models of industrial control systems, and can be used in cases when the number of vulnerabilities and measures is large. The advantages of our framework are the following. Firstly, the framework includes an algorithm for efficiently finding the most dangerous vulnerabilities in the system. Secondly, the problem of eliminating these vulnerabilities can provably be casted as a minimization of a linear function subject to a submodular constraint. This implies that the suboptimal solution of the problem, with guaranteed performance, can be found using a fast greedy algorithm. The applicability of the framework is demonstrated through simulations on an industrial control system used for regulating temperature within a building

  • 2.
    Milosevic, Jezdimir
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    A Security Index for Actuators Based on Perfect Undetectability: Properties and Approximation2019In: 2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018, Institute of Electrical and Electronics Engineers Inc. , 2019, p. 235-241Conference paper (Refereed)
    Abstract [en]

    A novel security index based on the definition of perfect undetectability is proposed. The index is a tool that can help a control system operator to localize the most vulnerable actuators in the network. In particular, the security index of actuator i represents the minimal number of sensors and actuators that needs to be compromised in addition to i, such that a perfectly undetectable attack is possible. A method for computing this index for small scale systems is derived, and difficulties with the index once the system is of large scale are outlined. An upper bound for the index that overcomes these difficulties is then proposed. The theoretical developments are illustrated on a numerical example. 

  • 3.
    Milosevic, Jezdimir
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tanaka, Takashi
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Analysis and Mitigation of Bias Injection Attacks Against a Kalman Filter2017In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 50, no 1, p. 8393-8398Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider a state estimation problem for stochastic linear dynamical systems in the presence of bias injection attacks. A Kalman filter is used as an estimator, and a chi-squared test is used to detect anomalies. We first show that the impact of the worst-case bias injection attack in a stochastic setting can be analyzed by a deterministic quadratically constrained quadratic program, which has an analytical solution. Based on this result, we propose a criterion for selecting sensors to secure in order to mitigate the attack impact. Furthermore, we derive a condition on the necessary number of sensors to secure in order for the impact to be less than a desired threshold.

  • 4.
    Milosevic, Jezdimir
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Umsonst, David
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Quantifying the Impact of Cyber-Attack Strategies for Control Systems Equipped with an Anomaly Detector2018In: 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 331-337, article id 8550188Conference paper (Refereed)
    Abstract [en]

    Risk assessment is an inevitable step in the implementation of cost-effective security strategies for control systems. One of the difficulties of risk assessment is to estimate the impact cyber-attacks may have. This paper proposes a framework to estimate the impact of several cyber-attack strategies against a dynamical control system equipped with an anomaly detector. In particular, we consider denial of service, sign alternation, rerouting, replay, false data injection, and bias injection attack strategies. The anomaly detectors we consider are stateless, cumulative sum, and multivariate exponentially weighted moving average detectors. As a measure of the attack impact, we adopt the infinity norm of critical states after a fixed number of time steps. For this measure and the aforementioned anomaly detectors, we prove that the attack impact for all of the attack strategies can be reduced to the problem of solving a set of convex minimization problems. Therefore, the exact value of the attack impact can be obtained easily. We demonstrate how our modeling framework can be used for risk assessment on a numerical example.

  • 5.
    Müller, Matias I.
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Milosevic, Jezdimir
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    A Risk-Theoretical Approach to H2-Optimal Control under Covert Attacks2018In: 57th IEEE Conference on Decision and Control, IEEE , 2018, p. 4553-4558Conference paper (Refereed)
    Abstract [en]

    We consider the control design problem of optimizing the H-2 performance of a closed-loop system despite the presence of a malicious covert attacker. It is assumed that the attacker has incomplete knowledge on the true process we are controlling. To account for this uncertainty, we employ different measures of risk from the so called family of coherent measures of risk. In particular, we compare the closed-loop performance when a nominal value is used, with three different measures of risk: average risk, worst-case scenario and conditional valueat- risk (CVaR). Additionally, applying the approach from a previous work, we derive a convex formulation for the control design problem when CVaR is employed to quantify the risk. A numerical example illustrates the advantages of our approach.

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