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  • 1.
    Adaldo, Antonio
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Liuzza, Davide
    Univ Sannio, Dept Engn, I-82100 Benevento, Italy..
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Cloud-Supported Formation Control of Second-Order Multiagent Systems2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 4, s. 1563-1574Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper addresses a formation problem for a network of autonomous agents with second-order dynamics and bounded disturbances. Coordination is achieved by having the agents asynchronously upload (download) data to (from) a shared repository, rather than directly exchanging data with other agents. Well-posedness of the closed-loop system is demonstrated by showing that there exists a lower bound for the time interval between two consecutive agent accesses to the repository. Numerical simulations corroborate the theoretical results.

  • 2.
    Demirel, Burak
    et al.
    Paderborn Univ, Chair Automat Control EIME, D-33098 Paderborn, Germany..
    Ghadimi, Euhanna
    Huawei Technol Sweden AB, SE-16494 Kista, Sweden..
    Quevedo, Daniel E.
    Paderborn Univ, Chair Automat Control EIME, D-33098 Paderborn, Germany..
    Johansson, Mikael
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Optimal Control of Linear Systems With Limited Control Actions: Threshold-Based Event-Triggered Control2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 3, s. 1275-1286Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a nonconvex domain. In this paper, we first provide an exact solution to this nonconvex problem by solving an exponential number of quadratic programs. To reduce computational complexity, we then propose two efficient heuristic algorithms based on greedy search and the alternating direction method of multipliers technique. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we further provide a complete stability analysis of receding horizon control that uses finite-horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.

  • 3. Guo, Meng
    et al.
    Bechlioulis, Charalampos P.
    Kyriakopoulos, Kostas J.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, Centrum för autonoma systen, CAS.
    Hybrid Control of Multiagent Systems With Contingent Temporal Tasks and Prescribed Formation Constraints2017Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 4, nr 4, s. 781-792Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we present a distributed hybrid control strategy for multiagent systems with contingent temporal tasks and prescribed formation constraints. Each agent is assigned a local task given as a linear temporal logic formula. In addition, two commonly seen kinds of cooperative robotic tasks, namely, service and formation, are requested and exchanged among the agents in real time. The service request is a short-term task provided by one agent to another. On the other hand, the formation request is a relative deployment requirement with predefined transient response imposed by an associated performance function. The proposed hybrid control strategy consists of four major components: 1) the contingent requests handlingmodule; 2) the real-time events monitoring module; 3) the local discrete plan synthesis module; and 4) the continuous control switching module, and it is shown that all local tasks and contingent service/formation requests are fulfilled. Finally, a simulated paradigm demonstrates the proposed control strategy.

  • 4.
    Guo, Ziyang
    et al.
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Hong Kong, Peoples R China. hi, Dawei.
    Shi, Dawei
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Shi, Ling
    Worst-Case Innovation-Based Integrity Attacks With Side Information on mote State Estimation2019Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 6, nr 1, s. 48-59Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we study the worst-case consequence of innovation-based tegrity attacks with side information in a remote state estimation enario where a sensor transmits its measurement to a remote estimator uipped with a false-data detector. If a malicious attacker is not only le to compromise the transmitted data packet but also able to measure e system state itself, the attack strategy can be designed based on e intercepted data, the sensing data, or alternatively the combined formation. Surprisingly, we show that launching attacks using the mbined information are not always optimal. First, we characterize the ealthiness constraints for different types of attack strategies to oid being noticed by the false-data detector. Then, we derive the olution of the remote estimation error covariance in the presence of tacks, based on which the worst-case attack policies are obtained by lving convex optimization problems. Furthermore, the closed-form pressions of the worst-case attacks are obtained for scalar systems d the attack consequences are compared with the existing work to termine which strategy is more critical in deteriorating system rformance. Simulation examples are provided to illustrate the alytical results.

  • 5.
    Hajiesmaili, Mohammad Hassan
    et al.
    Johns Hopkins Univ, Whiting Sch Engn, Baltimore, MD 21218 USA..
    Talebi Mazraeh Shahi, Mohammad Sadegh
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. K.
    Khonsari, Ahmad
    Univ Tehran, Dept Elect & Comp Engn, Tehran 1417614418, Iran.;Inst Res Fundamental Sci, Sch Comp Sci, Tehran 1953833511, Iran..
    Multiperiod Network Rate Allocation With End-to-End Delay Constraints2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 3, s. 1087-1097Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    QoS-aware networking applications such as real-time streaming and video surveillance systems require nearly fixed average end-to-end delay over long periods to communicate efficiently, although may tolerate some delay variations in short periods. This variability exhibits complex dynamics that makes rate control of such applications a formidable task. This paper addresses rate allocation for heterogeneous QoS-aware applications that preserves the long-term end-to-end delay constraint while seeking the maximum network utility cumulated over a fixed time interval. To capture the temporal dynamics of sources, we incorporate a novel time-coupling constraint in which delay sensitivity of sources is considered such that a certain end-to-end average delay for each source over a prespecified time interval is satisfied. We propose an algorithm, as a dual-based solution, which allocates source rates for the next time interval in a distributed fashion, given the knowledge of network parameters in advance. Also, we extend the algorithm to the case that the problem data is not known fully in advance to capture more realistic scenarios. Through numerical experiments, we show that our proposed algorithm attains higher average link utilization and a wider range of feasible scenarios in comparison with the best, to our knowledge, rate control schemes that may guarantee such constraints on delay.

  • 6.
    Linsenmayer, Steffen
    et al.
    Univ Stuttgart, Inst Syst Theory & Automat Control, D-70569 Stuttgart, Germany..
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för teknikvetenskap (SCI).
    Allgoewer, Frank
    Univ Stuttgart, Inst Syst Theory & Automat Control, D-70569 Stuttgart, Germany..
    Event-Based Vehicle Coordination Using Nonlinear Unidirectional Controllers2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 4, s. 1575-1584Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper presents a framework to control vehicle platoons with event-based communication and nonlinear controllers. The overall goal is to achieve a platoon that moves in a desired formation with a desired velocity and the convergence to this formation should be exponential while Zeno behavior has to be excluded. The set of admissible controllers for this problem is specified by the properties that they need to guarantee. These properties will be of a form such that they can be checked locally by every vehicle itself and heterogeneous controllers as well as heterogeneous possibly nonlinear dynamics of the vehicles in the platoon are allowed. The framework is shown to work with several communication networks and the set of networks will be characterized. Modifications that are necessary to cope with additive disturbances are described and a simulation example that shows the benefits of being able to use the framework in different networks is given.

  • 7.
    Liuzza, Davide
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Generalized PID Synchronization of Higher Order Nonlinear Systems With a Recursive Lyapunov Approach2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 4, s. 1608-1621Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we first study the global synchronization of nonlinear systems in the canonical control form with both distributed proportional-derivative and proportional-integral-derivative control actions of any order. To do so, we develop a constructive methodology and generate in an iterative way inequality constraints on the coupling matrices that guarantee the solvability of the problem or, in a dual form, provide the nonlinear weights on the coupling links between the agents such that the network synchronizes. The same methodology allows us to include a possible distributed integral action of any order to enhance the rejection of heterogeneous disturbances. The considered approach does not require any dynamic cancellation, thus preserving the original nonlinear dynamics of the agents. The results are then extended to linear and nonlinear systems admitting a canonical control transformation. Numerical simulations validate the theoretical results.

  • 8.
    Magnusson, Sindri
    et al.
    Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA..
    Qu, Guannan
    Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA..
    Fischione, Carlo
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Nätverk och systemteknik.
    Li, Na
    Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA..
    Voltage Control Using Limited Communication2019Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 6, nr 3, s. 993-1003Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In electricity distribution networks, the increasing penetration of renewable energy generation necessitates faster and more sophisticated voltage controls. Unfortunately, recent research shows that local voltage control fails in achieving the desired regulation, unless there is communication between the controllers. However, the communication infrastructure for distribution systems is less reliable and less ubiquitous compared to that for the bulk transmission system. In this paper, we design distributed voltage control that uses limited communication. That is, only neighboring buses need to communicate a few bits between each other for each control step. We investigate how these controllers can achieve the desired asymptotic behavior of the voltage regulation and we provide upper bounds on the number of bits that are needed to ensure a predefined accuracy of the regulation. Finally, we illustrate the results by numerical simulations.

  • 9. Meng, Ziyang
    et al.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Attitude Coordinated Control of Multiple Underactuated Axisymmetric Spacecraft2017Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 4, nr 4, s. 816-825Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Attitude coordinated control of multiple underactuated spacecraft is studied in this paper. We adopt the parametrization proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. We first propose a partial attitude coordinated controller with angular velocity commands. The controller is based on the exchange of each spacecraft's information with local neighbors and a self-damping term. Under a necessary and general connectivity assumption and by use of a novel Lyapunov function, we show that the symmetry axes of all spacecraft are eventually aligned. Full attitude control of multiple underactuated spacecraft is also considered and a discontinuous distributed control algorithm is proposed. It is shown that the proposed algorithm succeeds in achieving stabilization given that control parameters are chosen properly. Discussions on the cases without self damping are also provided for both partial and full attitude controls. Simulations are given to validate the theoretical results and different steadystate behaviors are observed.

  • 10.
    Ren, Xiaoqiang
    et al.
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Hong Kong, Peoples R China..
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Dawei
    Beijing Inst Technol, State Key Lab Intelligent Control & Decis Complex, Sch Automat, Beijing 100081, Peoples R China..
    Shi, Ling
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Hong Kong, Peoples R China..
    Quickest Change Detection in Adaptive Censoring Sensor Networks2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 1, s. 239-250Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of quickest change detection with communication rate constraints is studied. A network of wireless sensors with limited computation capability monitors the environment and sends observations to a fusion center via wireless channels. At an unknown time instant, the distributions of observations at all the sensor nodes change simultaneously. Due to limited energy, the sensors cannot transmit at all the time instants. The objective is to detect the change at the fusion center as quickly as possible, subject to constraints on false detection and average communication rate between the sensors and the fusion center. A minimax formulation is proposed. The cumulative sum (CuSum) algorithm is used at the fusion center and censoring strategies are used at the sensor nodes. The censoring strategies, which are adaptive to the CuSum statistic, are fed back by the fusion center. The sensors only send observations that fall into prescribed sets to the fusion center. This CuSum adaptive censoring (CuSum-AC) algorithm is proved to be an equalizer rule and to be globally asymptotically optimal for any positive communication rate constraint, as the average run length to false alarm goes to infinity. It is also shown, by numerical examples, that the CuSum-AC algorithm provides a suitable trade-off between the detection performance and the communication rate.

  • 11.
    Stankovic, Milos S.
    et al.
    Univ Belgrade, Sch Elect Engn, Innovat Ctr, Belgrade, Serbia..
    Stankovic, Srdjan S.
    Univ Belgrade, Sch Elect Engn, Belgrade, Serbia.;Vlatacom Inst, Belgrade, Serbia..
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Asynchronous Distributed Blind Calibration of Sensor Networks Under Noisy Measurements2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 1, s. 571-582Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, a novel distributed algorithm for asynchronous blind macro-calibration in sensor networks with noisy measurements is proposed. The algorithm is formulated as a set of instrumental variable type recursions for estimating parameters of sensor calibration functions. It is proved using asynchronous stochastic approximation arguments and properties of block-diagonally dominant matrices that the algorithm achieves asymptotic consensus for sensor gains and offsets in the mean square sense and with probability one. Recommendations for system design in terms of the choice of a priori tunable weights are provided. Special attention is paid to the situation when a subset of sensors in the network (reference sensors) remains with fixed characteristics. In the case of only one reference sensor, convergence of the remaining sensors to its characteristics is proved. In the case of more than one reference sensor, it is proved that the calibration parameters converge to points that depend only on the characteristics of the reference sensors and the network properties.

  • 12.
    Terelius, Håkan
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Peer-to-Peer Gradient Topologies in Networks With Churn2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 4, s. 2085-2095Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate the network topology convergence in a peer-to-peer (P2P) network system, where the goal of the system is to maximize live-streaming performance. The P2P system constructs a gradient overlay topology, characterized by a directed graph, where each node prefers neighbors containing higher utility values such that paths of increasing utilities emerge in the network topology. The gradient overlay network is built using gossiping and a preference function that samples nodes from a uniform random peer sampling service. Conditions for convergence to a gradient topology is derived, including the expected convergence time, and a threshold on the churn rate is provided for a gradient topology to emerge. Finally, a live-streaming video distribution experiment illustrates the benefits of constructing and utilizing the gradient topology for information dissemination in P2P systems.

  • 13.
    Wei, Jieqiang
    et al.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Yi, Xinlei
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Sandberg, Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Johansson, Karl Henrik
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik.
    Nonlinear Consensus Protocols With Applications to Quantized Communication and Actuation2019Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 6, nr 2, s. 598-608Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Nonlinearities are present in all real applications. Two types of general nonlinear consensus protocols are considered in this paper, namely, the systems with nonlinear communication and actuator constraints. The solutions of the systems are understood in the sense of Filippov to handle the possible discontinuity of the controllers. For each case, we prove the asymptotic stability of the systems with minimal assumptions on the nonlinearity, for both directed and undirected graphs. These results extend the literature to more general nonlinear dynamics and topologies. As applications of established theorems, we interpret the results on quantized consensus protocols.

  • 14.
    Yang, Tao
    et al.
    Univ North Texas, Dept Elect Engn, Denton, TX 76203 USA..
    Wu, Di
    Pacific Northwest Natl Lab, Richland, WA 99352 USA..
    Fang, Huazhen
    Univ Kansas, Dept Mech Engn, Lawrence, KS 66045 USA..
    Ren, Wei
    Univ Calif Riverside, Dept Elect Engn, Riverside, CA 92521 USA..
    Wang, Hong
    Oak Ridge Natl Lab, Oak Ridge, TN 37932 USA..
    Hong, Yiguang
    Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China..
    Johansson, Karl H.
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Reglerteknik. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Distributed Energy Resource Coordination Over Time-Varying Directed Communication Networks2019Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 6, nr 3, s. 1124-1134Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we consider the optimal coordination problem for distributed energy resources (DERs), including distributed generators and energy storages. We first propose an algorithm based on the push-sum and gradient method to solve the optimal DER coordination problem in a distributed manner. In the proposed algorithm, each DER only maintains a set of variables and updates them through information exchange with a few neighboring DERs over a time-varying directed communication network. We show that the proposed distributed algorithm with appropriately chosen diminishing step sizes solves the optimal DER coordination problem if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, in order to improve the convergence speed and to reduce the communication burden, we propose an accelerated distributed algorithm with a fixed step size. We show that the new proposed algorithm exponentially solves the optimal DER coordination problem if the cost functions satisfy an additional assumption and the selected step size is less than a certain critical value. Both proposed distributed algorithms are validated and evaluated using the IEEE 39-bus system.

  • 15.
    Zhang, Heng
    et al.
    Huaihai Inst Technol, Lianyungang, Peoples R China..
    Qi, Yifei
    Zhejiang Univ, State Key Lab Ind Control Technol, Hangzhou, Zhejiang, Peoples R China..
    Wu, Junfeng
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, Centrum för autonoma systen, CAS. KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.
    Fu, Lingkun
    Zhejiang Univ, State Key Lab Ind Control Technol, Hangzhou, Zhejiang, Peoples R China..
    He, Lidong
    Zhejiang Univ, State Key Lab Ind Control Technol, Hangzhou, Zhejiang, Peoples R China..
    DoS Attack Energy Management Against Remote State Estimation2018Inngår i: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, nr 1, s. 383-394Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper considers a remote state estimation problem, where a sensor measures the state of a linear discrete-time process and has computational capability to implement a local Kalman filter based on its own measurements. The sensor sends its local estimates to a remote estimator over a communication channel that is exposed to a Denial-of-Service (DoS) attacker. The DoS attacker, subject to limited energy budget, intentionally jams the communication channel by emitting interference noises with the purpose of deteriorating estimation performance. In order to maximize attack effect, following the existing answer to "when to attack the communication channel", in this paper we manage to solve the problem of "how much power the attacker should use to jam the channel in each time". For the static attack energy allocation problem, when the system matrix is normal, we derive a sufficient condition for when the maximum number of jamming operations should be used. The associated jamming power is explicitly provided. For a general system case, we propose an attack power allocation algorithm and show the computational complexity of the proposed algorithm is not worse than O(T), where T is the length of the time horizon considered. When the attack can receive the real-time ACK information, we formulate a dynamic attack energy allocation problem, and transform it to a Markov Decision Process to find the optimal solution.

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