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  • 1. Hosseini, M.
    et al.
    Tanaka, Takashi
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gupta, V.
    Designing optimal watermark signal for a stealthy attacker2017In: 2016 European Control Conference, ECC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 2258-2262, article id 7810627Conference paper (Refereed)
    Abstract [en]

    Consider a process being controlled remotely by a controller. Let an attacker have access to the communication channel so that she is able to replace the signal transmitted by the controller with any signal she wishes. The attacker wishes to degrade the control performance maximally without being detected. The controller wishes to detect the presence of the attacker by watermarking signaling information in the control input without degrading the control performance. There are no other assumptions on the capabilities of the attacker and the controller. We present an information theoretic formulation of the problem. Our main result is to show that in the one step version of the problem, if the watermark is a Gaussian distributed random variable, then the maximal performance degradation for any given level of stealthiness for the attacker is achieved when the attacker replaces the control input with the realization of a Gaussian random variable. Conversely, we show the watermark signal that minimizes the stealthiness of a Gaussian attacker is also Gaussian.

  • 2. Leong, A. S.
    et al.
    Quevedo, D. E.
    Tanaka, Takashi
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Dey, S.
    Ahlén, A.
    Event-Based Transmission Scheduling and LQG Control Over a Packet Dropping Link2017In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 50, no 1, p. 8945-8950Article in journal (Refereed)
    Abstract [en]

    This paper studies a joint transmission scheduling and controller design problem, which minimizes a linear combination of the control cost and expected energy usage of the sensor. Assuming that the sensor transmission decisions are event-based and determined using the random estimation error covariance information available to the controller, we show a separation in the design of the transmission scheduler and controller. The optimal controller is given as the solution to an LQG-type problem, while the optimal transmission policy is a threshold policy on the estimation error covariance at the controller.

  • 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.
    Milošević, Jezdimir
    et al.
    KTH.
    Tanaka, Takashi
    KTH.
    Sandberg, Henrik
    KTH.
    Johansson, Karl H.
    KTH.
    Exploiting Submodularity in Security Measure Allocation for Industrial Control Systems2017In: Proceedings of the 1st ACM Workshop on the Internet of Safe Things, ACM , 2017, p. 64-69Conference paper (Refereed)
    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.

  • 5.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Esfahani, Peyman Mohajerin
    Mitter, Sanjoy K.
    LQG Control with Minimum Directed Information2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 7359-7364, article id 7799406Conference paper (Refereed)
    Abstract [en]

    We consider a framework of LQG optimal control in which Massey's directed information from the state sequence to the control sequence is minimized The use of directed information in this study is motivated by the data-rate minimization in quantized LQG control. We show that an optimal control policy in our framework can be realized by a simple three stage architecture comprising (i) a linear sensor with additive Gaussian noise, (ii) a Kalman filter, and (iii) a certainty equivalence controller. This result can be viewed as an integration of two previously known separation theorems: the filter-controller separation theorem in the standard LQG control theory, and the sensor-filter separation theorem that arises in zero-delay rate-distortion theory for Gauss-Markov sources. A tractable computational algorithm based on semidefinite programming is proposed to synthesize an optimal policy.

  • 6.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gupta, Vijay
    Incentivizing Truth-Telling in MPC-based Load Frequency Control2016In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 1549-1555, article id 7798486Conference paper (Refereed)
    Abstract [en]

    We present a mechanism for socially efficient implementation of model predictive control (MPC) algorithms for load frequency control (LFC) in the presence of self-interested power generators. Specifically, we consider a situation in which the system operator seeks to implement an MPC-based LFC for aggregated social cost minimization, but necessary information such as individual generators' cost functions is privately owned. Without appropriate monetary compensation mechanisms that incentivize truth-telling, self-interested market participants may be inclined to misreport their private parameters in an effort to maximize their own profits, which may result in a loss of social welfare. The main challenge in our framework arises from the fact that every participant's strategy at any time affects the future state of other participants; the consequences of such dynamic coupling has not been fully addressed in the literature on online mechanism design. We propose a class of real-time monetary compensation schemes that incentivize market participants to report their private parameters truthfully at every time step, which enables the system operator to implement MPC-based LFC in a socially optimal manner.

  • 7.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Oechtering, T. J.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Rate of prefix-free codes in LQG control systems2016In: 2016 IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, Vol. 2016, p. 2399-2403, article id 7541729Conference paper (Refereed)
    Abstract [en]

    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.

  • 8.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Information Science and Engineering.
    Optimal Block Length for Data-Rate Minimization in Networked LQG Control2016In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 49, no 22, p. 133-138Article in journal (Refereed)
    Abstract [en]

    We consider a discrete-time networked LQG control problem in which state information must be transmitted to the controller over a noiseless binary channel using prefix-free codewords. Quantizer, encoder and controller are jointly designed to minimize average data-rate while satisfying required LQG control performance. We study the effects of selecting large block-lengths (data transmission intervals) from the perspectives of information-theoretic advantage due to coding efficiency and control-theoretic disadvantage due to delay. In particular, we demonstrate that the performance of networked control scheme by Tanaka et al. (2016) can be improved by adjusting the block-length optimally. As a byproduct of this study, we also show that the data-rate theorem for mean-square stability similar to Nair and Evans (2004) can be recovered by considering sufficiently large block-lengths.

  • 9.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kim, Kwang-Ki K.
    Parrilo, Pablo A.
    Mitter, Sanjoy K.
    Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 4, p. 1896-1910Article in journal (Refereed)
    Abstract [en]

    Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.

  • 10.
    Tanaka, Takashi
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Information Science and Engineering.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Directed information and privacy loss in cloud-based control2017In: Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1666-1672, article id 7963192Conference paper (Refereed)
    Abstract [en]

    We consider a cloud-based control framework in which individual clients own their local plants that must be controlled by a public authority. Individual clients desire to keep the local state information as private as possible, as long as the cloud-based controller can provide a given level of quality of service. Based on an axiomatic argument, we show that Kramer's notion of causally conditioned directed information from the state random variable to a random variable disclosed to the public authority is an appropriate measure of privacy loss. For a special case with the Linear-Quadratic-Gaussian (LQG) setting, we provide a procedure to construct a 'privacy filter' that attains the optimal trade-off between privacy loss and control quality.

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