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  • 1.
    Båberg, Fredrik
    et al.
    KTH, School of Computer Science and Communication (CSC), Robotics, perception and learning, RPL. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Petter, Ögren
    KTH, School of Electrical Engineering and Computer Science (EECS), Robotics, perception and learning, RPL. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Formation Obstacle Avoidance using RRT and Constraint Based Programming2017In: 2017 IEEE International Symposium on Safety, Security and Rescue Robotics (SSRR), IEEE conference proceedings, 2017, article id 8088131Conference paper (Refereed)
    Abstract [en]

    In this paper, we propose a new way of doing formation obstacle avoidance using a combination of Constraint Based Programming (CBP) and Rapidly Exploring Random Trees (RRTs). RRT is used to select waypoint nodes, and CBP is used to move the formation between those nodes, reactively rotating and translating the formation to pass the obstacles on the way. Thus, the CBP includes constraints for both formation keeping and obstacle avoidance, while striving to move the formation towards the next waypoint. The proposed approach is compared to a pure RRT approach where the motion between the RRT waypoints is done following linear interpolation trajectories, which are less computationally expensive than the CBP ones. The results of a number of challenging simulations show that the proposed approach is more efficient for scenarios with high obstacle densities.

  • 2.
    Duberg, Daniel
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Jensfelt, Patric
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    The Obstacle-restriction Method for Tele-operation of Unmanned Aerial Vehicles with Restricted Motion2018In: 2018 15TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION, ROBOTICS AND VISION (ICARCV), IEEE , 2018, p. 266-273Conference paper (Refereed)
    Abstract [en]

    This paper presents a collision avoidance method for tele-operated unmanned aerial vehicles (UAVs). The method is designed to assist the operator at all times, such that the operator can focus solely on the main objectives instead of avoiding obstacles. We restrict the altitude to be fixed in a three dimensional environment to simplify the control and operation of the UAV. The method contributes a number of desired properties not found in other collision avoidance systems for tele-operated UAVs. Our method i) can handle situations where there is no input from the user by actively stopping and proceeding to avoid obstacles, ii) allows the operator to slide between prioritizing staying away from objects and getting close to them in a safe way when so required, and iii) provides for intuitive control by not deviating too far from the control input of the operator. We demonstrate the effectiveness of the method in real world experiments with a physical hexacopter in different indoor scenarios. We also present simulation results where we compare controlling the UAV with and without our method activated.

  • 3. Guo, Meng
    et al.
    Bechlioulis, Charalampos P.
    Kyriakopoulos, Kostas J.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Hybrid Control of Multiagent Systems With Contingent Temporal Tasks and Prescribed Formation Constraints2017In: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 4, no 4, p. 781-792Article in journal (Refereed)
    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, Meng
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Boskos, Dimitris
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Tumova, Jana
    KTH, School of Electrical Engineering and Computer Science (EECS), Robotics, perception and learning, RPL.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Distributed hybrid control synthesis for multi-agent systems from high-level specifications2018In: Control Subject to Computational and Communication Constraints, Springer Verlag , 2018, 475, p. 241-260Chapter in book (Refereed)
    Abstract [en]

    Current control applications necessitate in many cases the consideration of systems with multiple interconnected components. These components/agents may need to fulfill high-level tasks at a discrete planning layer and also coupled constraints at the continuous control layer. Toward this end, the need for combined decentralized control at the continuous layer and planning at the discrete layer becomes apparent. While there are approaches that handle the problem in a top-down centralized manner, decentralized bottom-up approaches have not been pursued to the same extent. We present here some of our results for the problem of combined, hybrid control and task planning from high-level specifications for multi-agent systems in a bottom-up manner. In the first part, we present some initial results on extending the necessary notion of abstractions to multi-agent systems in a distributed fashion. We then consider a setup where agents are assigned individual tasks in the form of linear temporal logic (LTL) formulas and derive local task planning strategies for each agent. In the last part, the problem of combined distributed task planning and control under coupled continuous constraints is further considered.

  • 5.
    Heshmati-Alamdari, Shahab
    et al.
    Natl Tech Univ Athens, Dept Mech Engn, Control Syst Lab, 9 Heroon Polytech St, Zografos 15780, Greece..
    Bechlioulis, Charalampos P.
    Natl Tech Univ Athens, Dept Mech Engn, Control Syst Lab, 9 Heroon Polytech St, Zografos 15780, Greece..
    Karras, George C.
    Natl Tech Univ Athens, Dept Mech Engn, Control Syst Lab, 9 Heroon Polytech St, Zografos 15780, Greece..
    Nikou, Alexandros
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH Royal Inst Technol, KTH Ctr Autonomous Syst, SE-10044 Stockholm, Sweden..
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH Royal Inst Technol, KTH Ctr Autonomous Syst, SE-10044 Stockholm, Sweden..
    Kyriakopoulos, Kostas J.
    Natl Tech Univ Athens, Dept Mech Engn, Control Syst Lab, 9 Heroon Polytech St, Zografos 15780, Greece..
    A robust interaction control approach for underwater vehicle manipulator systems2018In: Annual Reviews in Control, ISSN 1367-5788, E-ISSN 1872-9088, Vol. 46, p. 315-325Article, review/survey (Refereed)
    Abstract [en]

    In underwater robotic interaction tasks (e.g., sampling of sea organisms, underwater welding, panel handling, etc) various issues regarding the uncertainties and complexity of the robot dynamic model, the external disturbances (e.g., sea currents), the steady state performance as well as the overshooting/undershooting of the interaction force error, should be addressed during the control design. Motivated by the aforementioned considerations, this paper presents a force/position tracking control protocol for an Underwater Vehicle Manipulator System (UVMS) in compliant contact with a planar surface, without incorporating any knowledge of the UVMS dynamic model, the exogenous disturbances or the contact stiffness model. Moreover, the proposed control framework guarantees: (i) certain predefined minimum speed of response, maximum steady state error as well as overshoot/undershoot concerning the force/position tracking errors, (ii) contact maintenance and (iii) bounded closed loop signals. Additionally, the achieved transient and steady state performance is solely determined by certain designer-specified performance functions/parameters and is fully decoupled from the control gain selection and the initial conditions. Finally, both simulation and experimental studies clarify the proposed method and verify its efficiency.

  • 6.
    Kokic, Mia
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Antonova, Rika
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Stork, Johannes
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Kragic, Danica
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Global Search with Bernoulli Alternation Kernel for Task-oriented Grasping Informed by Simulation2018Conference paper (Refereed)
  • 7.
    Lindemann, Lars
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH Royal Inst Technol, Sch Elect Engn & Comp Sci, Dept Automat Control, Malvinas Vag 10, SE-10044 Stockholm, Sweden..
    Robust control for signal temporal logic specifications using discrete average space robustness2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 101, p. 377-387Article in journal (Refereed)
    Abstract [en]

    Control systems that satisfy temporal logic specifications have become increasingly popular due to their applicability to robotic systems. Existing control methods, however, are computationally demanding, especially when the problem size becomes too large. In this paper, a robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed. We introduce discrete average space robustness, a novel quantitative semantic for signal temporal logic, that is directly incorporated into the cost function of the model predictive controller. The optimization problem entailed in this framework can be written as a convex quadratic program when no disjunctions are considered and results in a robust satisfaction of the specification. Furthermore, we define the predicate robustness degree as a new robustness notion. Simulations of a multi-agent system subject to complex specifications demonstrate the efficacy of the proposed method.

  • 8.
    Nikou, Alexandros
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Boskos, Dimitris
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Tumova, Jana
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    On the timed temporal logic planning of coupled multi-agent systems2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 97, p. 339-345Article in journal (Refereed)
    Abstract [en]

    This paper presents a fully automated procedure for controller synthesis for multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). First, a decentralized abstraction that provides a space and time discretization of the multi-agent system is designed. Second, by utilizing this abstraction and techniques from formal verification, we propose an algorithm that computes the individual runs which provably satisfy the high-level tasks. The overall approach is demonstrated in a simulation example conducted in MATLAB environment. 

  • 9.
    Nikou, Alexandros
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Boskos, Dimitris
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Tumova, Jana
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    On the timed temporal logic planning of coupled multi-agent systems2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 97, p. 339-345Article in journal (Refereed)
    Abstract [en]

    This paper presents a fully automated procedure for controller synthesis for multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). First, a decentralized abstraction that provides a space and time discretization of the multi agent system is designed. Second, by utilizing this abstraction and techniques from formal verification, we propose an algorithm that computes the individual runs which provably satisfy the high-level tasks. The overall approach is demonstrated in a simulation example conducted in MATLAB environment.

  • 10.
    Schlueter, Henning
    et al.
    Univ Stuttgart, Stuttgart, Germany..
    Schillinger, Philipp
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Buerger, Mathias
    Bosch Ctr Artificial Intelligence, Renningen, Germany..
    On the Design of Penalty Structures for Minimum-Violation LTL Motion Planning2018In: 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 4153-4158, article id 8619148Conference paper (Refereed)
    Abstract [en]

    This paper studies the problem of penalizing rule violation in the context of logic-based motion planning. Translating a given Linear Temporal Logic (LTL) rule into a penalty structure requires a design decision, since the discrete automata obtained from the rule do not provide a straightforward method to penalize rule violation. We propose a design method that explicitly specifies violation to allow for more flexibility in parametrization of desired behaviors and differentiation of penalty semantics. Case study results are shown in the context of an autonomous driving scenario.

  • 11.
    Selin, Magnus
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. Linkoping Univ, Dept Comp & Informat Sci, S-58183 Linkoping, Sweden.
    Tiger, Maths
    Linkoping Univ, Dept Comp & Informat Sci, S-58183 Linkoping, Sweden..
    Duberg, Daniel
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Heintz, Fredrik
    Linkoping Univ, Dept Comp & Informat Sci, S-58183 Linkoping, Sweden..
    Jensfelt, Patric
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Efficient Autonomous Exploration Planning of Large-Scale 3-D Environments2019In: IEEE Robotics and Automation Letters, ISSN 2377-3766, E-ISSN 1949-3045, Vol. 4, no 2, p. 1699-1706Article in journal (Refereed)
    Abstract [en]

    Exploration is an important aspect of robotics, whether it is for mapping, rescue missions, or path planning in an unknown environment. Frontier Exploration planning (FEP) and Receding Horizon Next-Best-View planning (RH-NBVP) are two different approaches with different strengths and weaknesses. FEP explores a large environment consisting of separate regions with ease, but is slow at reaching full exploration due to moving back and forth between regions. RH-NBVP shows great potential and efficiently explores individual regions, but has the disadvantage that it can get stuck in large environments not exploring all regions. In this letter, we present a method that combines both approaches, with FEP as a global exploration planner and RH-NBVP for local exploration. We also present techniques to estimate potential information gain faster, to cache previously estimated gains and to exploit these to efficiently estimate new queries.

  • 12.
    Theodosis, Dionysios
    et al.
    Natl Tech Univ Athens, Dept Math, Athens 15780, Greece..
    Boskos, Dimitris
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Tsinias, John
    Natl Tech Univ Athens, Dept Math, Athens 15780, Greece..
    Observer Design for Triangular Systems Under Weak Observability Assumptions2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 12, p. 4156-4171Article in journal (Refereed)
    Abstract [en]

    This paper presents results on the solvability of the observer design problem for general nonlinear triangular systems with inputs, under weak observability assumptions. The local state estimation is exhibited by means of a delayed time-varying Luenberger-type system. In order to achieve the global estimation, a switching sequence of observers is designed.

  • 13.
    Verginis, Christos
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Mastellaro, Matteo
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Robust Cooperative Manipulation Without Force/Torque Measurements: Control Design and Experiments2019In: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865Article in journal (Refereed)
    Abstract [en]

    This paper presents two novel control methodologies for the cooperative manipulation of an object by  N robotic agents. First, we design an adaptive control protocol which employs quaternion feedback for the object orientation to avoid potential representation singularities. Second, we propose a control protocol that guarantees predefined transient and steady-state performance for the object trajectory. Both methodologies are decentralized, since the agents calculate their own signals without communicating with each other, as well as robust to external disturbances and model uncertainties. Moreover, we consider that the grasping points are rigid and avoid the need for force/torque measurements. Load distribution is also included via a grasp matrix pseudoinverse to account for potential differences in the agents’ power capabilities. Finally, simulation and experimental results with two robotic arms verify the theoretical findings.

  • 14.
    Verginis, Christos
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Nikou, Alexandros
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Robust formation control in SE(3) for tree-graph structures with prescribed transient and steady state performance2019In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 103, p. 538-548Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE(3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach.

  • 15.
    Yang, Guang-Zhong
    et al.
    Imperial Coll London, Hamlyn Ctr Robot Surg, London, England..
    Dario, Paolo
    Scuola Super Sant Anna, Biomed Robot, Pisa, Italy..
    Kragic, Danica
    KTH, School of Electrical Engineering and Computer Science (EECS), Robotics, perception and learning, RPL. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS.
    Social robotics-Trust, learning, and social interaction2018In: Science Robotics, ISSN 2470-9476, Vol. 3, no 21, article id UNSP eaau8839Article in journal (Other academic)
  • 16.
    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, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, 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 Estimation2018In: IEEE Transactions on Big Data, ISSN 2325-5870, E-ISSN 2168-6750, Vol. 5, no 1, p. 383-394Article in journal (Refereed)
    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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