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  • 1. Farokhi, Farhad
    et al.
    Milosevic, Jezdimir
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Optimal State Estimation with Measurements Corrupted by Laplace Noise2016Ingår i: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, s. 302-307, artikel-id 7798286Konferensbidrag (Refereegranskat)
    Abstract [en]

    Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter.

  • 2.
    Gracy, Sebin
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Milosevic, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Actuator Security Index for Structured Systems2020Ingår i: Proceedings 2020 American Control Conference, ACC 2020, Denver, CO, USA, July 1-3, 2020, Institute of Electrical and Electronics Engineers (IEEE) , 2020, s. 2993-2998Konferensbidrag (Refereegranskat)
    Abstract [en]

    Given a network with a set of vulnerable actuators (and sensors), the security index of an actuator equals the minimum number of sensors and actuators that needs to be compromised so as to conduct a perfectly undetectable attack using the said actuator. This paper deals with the problem of computing actuator security indices for discrete-time LTI network systems, using a structured systems framework. We show that the actuator security index is generic, that is for almost all realizations the actuator security index remains the same. We refer to such an index as generic security index (generic index) of an actuator. Given that the security index quantifies the vulnerability of a network, the generic index is quite valuable for large scale energy systems. Our second contribution is to provide graph-theoretic conditions for computing the generic index. The said conditions are in terms of existence of linkings on appropriately-defined directed (sub)graphs. Based on these conditions, we present an algorithm for computing the generic index.

  • 3.
    Gracy, Sebin
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Milosevic, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Security index based on perfectly undetectable attacks: Graph-theoretic conditions2021Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 134, artikel-id 109925Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The notion of security index quantifies the least effort involved in conducting perfectly undetectable attacks. Thus, the security index enables a systems operator to assess the vulnerability of a component, informs sensor placement strategies, and helps in deciding the feasibility of secure estimators and fault detectors. In this paper, we investigate the (possible) variation in this index as a consequence of variation in the system parameters. To this end, we adopt a structured systems approach, typically represented by a directed graph, with the edges of the said graph being in one-to-one correspondence with the system parameters. We first show that the security index is generic. That is, for almost all choices of edge weights, the security index of a component remains the same. We refer to such an index as the generic security index. Secondly, we derive graph-theoretic conditions (and based on those an algorithm) for computing the generic security index. Third, we provide graph-theoretic conditions for computing lower (resp. upper) bounds on the values that the security index of a component can take for all nonzero choices of the edge weights of the directed graph. Finally, we provide a brute force search method for calculating the said bounds.

  • 4.
    Gracy, Sebin
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Milosevic, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Security index based on perfectly undetectable attacks: Graph-theoretic conditions- Supplementary Material2021Övrigt (Refereegranskat)
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  • 5.
    Milosevic, Jezdemir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Estimating the impact of cyber-attack strategies for stochastic networked control systems2020Ingår i: IEEE Transactions on Control of Network Systems, E-ISSN 2325-5870, Vol. 7, nr 2, s. 747-757, artikel-id 8827641Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Risk assessment is an inevitable step in implementation of a cyber-defense strategy. An important part of this assessment is to reason about the impact of possible attacks. In this paper, we study the problem of estimating the impact of cyber-attacks in stochastic linear networked control systems. For the stealthiness constraint, we adopt the Kullback-Leibler divergence between attacked and nonattacked residual sequences. Two impact metrics are considered: the probability that some of the critical states leave a safety region and the expected value of the infinity norm of the critical states. For the first metric, we prove that the optimal value of the impact estimation problem can be calculated by solving a set of convex problems. For the second, we derive efficiency to calculate lower and upper bounds. Finally, we show compatibility of our framework with a number of attack strategies proposed in the literature and demonstrate how it can be used for risk assessment in an example.

  • 6.
    Milosevic, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Model Based Impact Analysis and Security Measure Allocation for Control Systems2018Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [sv]

    Att säkerställa och förbättra cybersäkerheten hos industriella styrsystem är av stor vikt för samhällssäkerheten. Det är känt att det förekommer sårbar-heter hos den här typen av system, som om de utnyttjas kan leda till allvarliga konsekvenser. Till exempel kan cyberattacker mot industriella styrsystem leda till storskaliga strömavbrott, dricksvattenbrist och störningar i olje- och gasproduktion. Av dessa skäl har de här problemen fått stor uppmärksamhet inom såväl forskningen som hos myndigheter och industrin. Den här avhandlingen motiveras främst av att de åtgärder som kan vidtas för att skydda industriella styrsystem ofta är kostsamma. I många fall är det därför inte möjligt att åtgärda alla sårbarheter som kan hittas hos systemen. Man behöver därför ta hänsyn till två problem. Till att börja med, hur man kan identifiera vilka sårbarheter, eller kombinationer av dessa, som det är mest kritiskt att förhindra angrepp mot. En viktig del av denna analys är att beräkna effekten av sådana angrepp. Detta problem behandlas i avhandlingens första del. Nästa problem är att fördela en budget för säkerhetsåtgärder för att förebygga de mest kritiska sårbarheterna, vilket behandlas i avhandlingens andra del. Avhandlingens första bidrag är ett ramverk för att bedöma effekten av angrepp mot industriella styrsystem. Här betraktar vi industriella styrsystem som både har till uppgift att reglera och att övervaka. För system med regler-uppgifter föreslår vi ett ramverk för att uppskatta effekterna av flera olika angreppsstrategier. Vi visar att beräkningen av effekten av samtliga strategier kan reduceras till att lösa en uppsättning konvexa minimeringsproblem. Eftersom lösningsalgoritmer för sådana problem är välkända så kan exakta värden enkelt beräknas. För industriella styrsystem med övervakningsuppgifter analyserar vi effekten av angrepp i form av injektion av bias. Vi bevisar attdenna effekt kan fås som lösningen till ett så kallat kvadratiskt programmeringsproblem med kvadratiska bivillkor, som går att lösa exakt på ett effektivt sätt. Vi demonstrerar resultaten i numeriska exempel. Avhandlingens andra bidrag är en flexibel modelleringsmetod för resurs-fördelning av säkerhetsåtgärder. Metoden vi föreslår är lämpad för dynamiska modeller av industriella styrsystem och löser resursfördelningsproblemet när antalet sårbarbeter och åtgärder är stort. Den föreslagna metoden kan effektivt identifiera de farligaste sårbarheterna i systemet. Sedan visar vi hur problemet med att eliminera dessa sårbarheter kan formuleras som en minimering av en linjär funktion med submodulära bivillkor. Detta innebär att man med garanterad prestanda kan hitta en sub otimal lösning med hjälp aven snabb så kallad girig algorithm. Vi demonstrerar att våra metoder går att tillämpa genom simuleringar av ett industriellt temperatur regleringssystem.

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  • 7.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Dahan, M.
    Amin, S.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    A Network Monitoring Game with Heterogeneous Component Criticality Levels2019Ingår i: Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc. , 2019, s. 4379-4384Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider an attacker-operator game for monitoring a large-scale network that is comprised of components that differ in their criticality levels. In this zero-sum game, the operator seeks to position a limited number of sensors to monitor the network against the attacker who strategically targets a network component. The operator (resp. attacker) seeks to minimize (resp. maximize) the network loss. To study the properties of mixed-strategy Nash Equilibria of this game, we first study two simple instances: When component sets monitored from individual sensor locations are mutually disjoint; When only a single sensor is positioned, but with possibly overlapping monitoring component sets. Our analysis reveals new insights on how criticality levels impact the players equilibrium strategies. Next, we extend a previously developed approach to obtain an approximate Nash equilibrium in the general case. This approach uses solutions to minimum set cover and maximum set packing problems to construct an approximate Nash equilibrium. Finally, we implement a column generation procedure to improve this solution and numerically evaluate the performance of our approach. 

  • 8.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Gracy, Sebin
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    On actuator security indices2020Ingår i: 14th International Conference on Critical Information Infrastructures Security, CRITIS 2019, Springer Nature , 2020, s. 182-187Konferensbidrag (Refereegranskat)
    Abstract [en]

    Actuator security indices are developed for risk assessment purposes. Particularly, these indices can tell a system operator which of the actuators in a critical infrastructure network are the most vulnerable to cyber-attacks. Once the operator has this information, he/she can focus the security budget to protect these actuators. In this short paper, we first revisit one existing definition of an actuator security index, and then discuss possible directions for future research.

  • 9.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    A Security Index for Actuators Based on Perfect Undetectability: Properties and Approximation2019Ingår i: 2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018, Institute of Electrical and Electronics Engineers (IEEE), 2019, s. 235-241Konferensbidrag (Refereegranskat)
    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. 

  • 10.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Tanaka, Takashi
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Analysis and Mitigation of Bias Injection Attacks Against a Kalman Filter2017Ingår i: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 50, nr 1, s. 8393-8398Artikel i tidskrift (Refereegranskat)
    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.

  • 11.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Teixeira, Andre
    Uppsala Univ, Dept Engn Sci, Signals & Syst, S-75236 Uppsala, Sweden..
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Actuator Security Indices Based on Perfect Undetectability: Computation, Robustness, and Sensor Placement2020Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 65, nr 9, s. 3816-3831Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose an actuator security index that can be used to localize and protect vulnerable actuators in a networked control system. Particularly, the security index of an actuator equals to the minimum number of sensors and actuators that need to be compromised, such that a perfectly undetectable attack against that actuator can be conducted. We derive a method for computing the index in small-scale systems and show that the index can potentially be increased by placing additional sensors. The difficulties that appear once the system is of a large-scale are then outlined: The index is NP-hard to compute, sensitive with respect to system variations, and based on the assumption that the attacker knows the entire system model. To overcome these difficulties, a robust security index is introduced. The robust index can characterize actuators vulnerable in any system realization, can be calculated in polynomial time, and can be related to limited model knowledge attackers. Additionally, we analyze two sensor placement problems with the objective to increase the robust indices. We show that the problems have submodular structures, so their suboptimal solutions with performance guarantees can be computed in polynomial time. Finally, we illustrate the theoretical developments through examples.

  • 12.
    Milosevic, Jezdimir
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Umsonst, David
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Johansson, Karl Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Quantifying the Impact of Cyber-Attack Strategies for Control Systems Equipped with an Anomaly Detector2018Ingår i: 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers (IEEE), 2018, s. 331-337, artikel-id 8550188Konferensbidrag (Refereegranskat)
    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.

  • 13.
    Miloševiç, Jezdimir
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Teixeira, André
    Tanaka, Takashi
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Security Measure Allocation for Industrial Control Systems: Exploiting Systematic Search Techniques and Submodularity2020Ingår i: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 30, nr 11, s. 4278-4302Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    To protect industrial control systems from cyberattacks, multiple layers of security measures need to be allocated to prevent critical security vulnerabilities. However, both finding the critical vulnerabilities and then allocating security measures in a cost‐efficient way become challenging when the number of vulnerabilities and measures is large. This paper proposes a framework that can be used once this is the case. In our framework, the attacker exploits security vulnerabilities to gain control over some of the sensors and actuators. The critical vulnerabilities are those that are not complex to exploit and can lead to a large impact on the physical world through the compromised sensors and actuators. To find these vulnerabilities efficiently, we propose an algorithm that uses the nondecreasing properties of the impact and complexity functions and properties of the security measure allocation problem to speed up the search. Once the critical vulnerabilities are located, the security measure allocation problem reduces to an integer linear program. Since integer linear programs are NP‐hard in general, we reformulate this problem as a problem of minimizing a linear set function subject to a submodular constraint. A polynomial time greedy algorithm can then be applied to obtain a solution with guaranteed approximation bound. The applicability of our framework is demonstrated on a control system used for regulation of temperature within a building.

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  • 14.
    Milošević, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Security metrics and allocation of security resources for control systems2020Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Achieving a sufficient level of security of control systems is very important, yet challenging. Firstly, control systems operate critical infrastructures vital for our society. Hence, attacks against them can result in dire consequences. Secondly, large numbers of security vulnerabilities typically exist in these systems, which makes them attractive targets of attacks. In fact, several attacks have already occurred. Thirdly, due to their specific nature, securing control systems can be costly. For example, their real time availability requirements complicate the deployment of security measures, and control system equipment with limited computational power is unsuited for many security solutions. Motivated by the necessity of control systems security, we study two security-related applications. The first application considers classifying and preventing security vulnerabilities. We aim to first characterize the most critical vulnerability combinations in a control system, and then prevent these combinations in a cost-effective manner. To characterize the critical vulnerability combinations, we develop an impact estimation framework. Particularly, we use a physical model of the control system to simulate the impact that attack strategies may have on the physical process. Our framework is compatible with a number of attack strategies proposed throughout the literature, and can be used to estimate the impact efficiently. To prevent critical vulnerability combinations in a cost-effective manner, we develop a security measure allocation framework. The framework includes an algorithm for systematically finding critical vulnerability combinations, and two approaches for allocating security measures that prevent these combinations cost-effectively. The second application considers actuator security. Actuators are vital components of control systems to protect, since they directly interact with the physical process. To evaluate the vulnerability of every actuator in a control system, we develop actuator security indices. These indices characterize resources that the attacker needs to compromise to conduct a perfectly undetectable attack against each actuator. We propose methods to compute the actuator security indices, show that the defender can improve the indices by allocating additional sensors, and discuss the robustness of the indices. We also study a sensor allocation game based on actuator security indices. The goal of studying this game is to develop a monitoring strategy that improves the indices. We derive an approximate Nash Equilibrium of the game, and present the cases when this approximate Nash Equilibrium becomes exact. We also outline the intuition behind this equilibrium, and discuss the ways to further improve the monitoring strategy from the equilibrium.

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  • 15.
    Milošević, Jezdimir
    et al.
    KTH.
    Tanaka, Takashi
    KTH.
    Sandberg, Henrik
    KTH.
    Johansson, Karl H.
    KTH.
    Exploiting Submodularity in Security Measure Allocation for Industrial Control Systems2017Ingår i: Proceedings of the 1st ACM Workshop on the Internet of Safe Things, ACM , 2017, s. 64-69Konferensbidrag (Refereegranskat)
    Abstract [en]

    Industrial control systems are cyber-physical systems that are used to operate critical infrastructures such as smart grids, traffic systems, industrial facilities, and water distribution networks. The digitalization of these systems increases their efficiency and decreases their cost of operation, but also makes them more vulnerable to cyber-attacks. In order to protect industrial control systems from cyber-attacks, the installation of multiple layers of security measures is necessary. In this paper, we study how to allocate a large number of security measures under a limited budget, such as to minimize the total risk of cyber-attacks. The security measure allocation problem formulated in this way is a combinatorial optimization problem subject to a knapsack (budget) constraint. The formulated problem is NP-hard, therefore we propose a method to exploit submodularity of the objective function so that polynomial time algorithms can be applied to obtain solutions with guaranteed approximation bounds. The problem formulation requires a preprocessing step in which attack scenarios are selected, and impacts and likelihoods of these scenarios are estimated. We discuss how the proposed method can be applied in practice.

  • 16.
    Müller, Matias I.
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Milosevic, Jezdimir
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    Rojas, Cristian R.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Intelligenta system, Reglerteknik.
    A Risk-Theoretical Approach to H2-Optimal Control under Covert Attacks2018Ingår i: 57th IEEE Conference on Decision and Control, IEEE , 2018, s. 4553-4558Konferensbidrag (Refereegranskat)
    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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