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  • 1.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Alderisio, Francesco
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Liuzza, Davide
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Shi, Guodong
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    di Bernardo, Mario
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Event-triggered pinning control of complex networks with switching topologies2014In: Proceedings of the 53rd annual IEEE Conference on Decision and Control, 2014, p. 2783-2788Conference paper (Refereed)
    Abstract [en]

    This paper investigates the problem of eventtriggered pinning control for the synchronization of networks of nonlinear dynamical agents onto a desired reference trajectory. The pinned agents are those that have access to the reference trajectory. We consider both static and switching topologies. We prove that the system is well posed and identify conditions under which the network achieves exponential convergence. A lower bound for the rate of convergence is also derived. Numerical examples demonstrating the effectiveness of the results are provided.

  • 2.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Alderisio, Francesco
    Liuzza, Davide
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    di Bernardo, Mario
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. University of Naples Federico II, Italy.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Event-Triggered Pinning Control of Switching Networks2015In: IEEE Transactions on Control of Network Systems, ISSN 2325-5870, Vol. 2, no 2, p. 204-213, article id 7098382Article in journal (Refereed)
    Abstract [en]

    This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy.

  • 3.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Liuzza, D.
    Dimarogonas, Dimos V.
    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.
    Coordination of multi-agent systems with intermittent access to a cloud repository2017In: Workshop on Sensing and Control for Autonomous Vehicles: Applications to Land, Water and Air Vehicles, 2017, Springer, 2017, Vol. 474, p. 453-471Conference paper (Refereed)
    Abstract [en]

    A cloud-supported multi-agent system is composed of autonomous agents required to achieve a common coordination objective by exchanging data over a shared cloud repository. The repository is accessed asychronously by different agents, and direct inter-agent commuication is not possible. This model is motivated by the problem of coordinating a fleet of autonomous underwater vehicles, with the aim to avoid the use of expensive and power-hungry modems for underwater communication. For the case of agents with integrator dynamics, a control law and a rule for scheduling the cloud access are formally defined and proven to achieve the desired coordination. A numerical simulation corroborate the theoretical results.

  • 4.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Liuzza, Davide
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Control of Multi-Agent Systems with Event-Triggered Cloud Access2015In: Proceedings of the 14th annual European Control Conference, 2015Conference paper (Refereed)
  • 5.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mansouri, S. S.
    Kanellakis, C.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Nikolakopoulos, G.
    Cooperative coverage for surveillance of 3D structures2017In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1838-1845Conference paper (Refereed)
    Abstract [en]

    In this article, we propose a planning algorithm for coverage of complex structures with a network of robotic sensing agents, with multi-robot surveillance missions as our main motivating application. The sensors are deployed to monitor the external surface of a 3D structure. The algorithm controls the motion of each sensor so that a measure of the collective coverage attained by the network is nondecreasing, while the sensors converge to an equilibrium configuration. A modified version of the algorithm is also provided to introduce collision avoidance properties. The effectiveness of the algorithm is demonstrated in a simulation and validated experimentally by executing the planned paths on an aerial robot.

  • 6.
    Adaldo, Antonio
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mansouri, Sina Sharif
    Lulea Univ Technol, Dept Comp Elect & Space Engn, Control Engn Div, Robot Grp, SE-97187 Lulea, Sweden..
    Kanellakis, Christoforos
    Lulea Univ Technol, Dept Comp Elect & Space Engn, Control Engn Div, Robot Grp, SE-97187 Lulea, Sweden..
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Nikolakopoulos, George
    Lulea Univ Technol, Dept Comp Elect & Space Engn, Control Engn Div, Robot Grp, SE-97187 Lulea, Sweden..
    Cooperative coverage for surveillance of 3D structures2017In: 2017 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS (IROS) / [ed] Bicchi, A Okamura, A, IEEE , 2017, p. 1838-1845Conference paper (Refereed)
    Abstract [en]

    In this article, we propose a planning algorithm for coverage of complex structures with a network of robotic sensing agents, with multi-robot surveillance missions as our main motivating application. The sensors are deployed to monitor the external surface of a 3D structure. The algorithm controls the motion of each sensor so that a measure of the collective coverage attained by the network is nondecreasing, while the sensors converge to an equilibrium configuration. A modified version of the algorithm is also provided to introduce collision avoidance properties. The effectiveness of the algorithm is demonstrated in a simulation and validated experimentally by executing the planned paths on an aerial robot.

  • 7.
    Ahmadi, Seyed Alireza
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Shames, Iman
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Scotton, Francesco
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Huang, Lirong
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Towards more efficient building energy management systems2012In: Proceedings - 2012 7th International Conference on Knowledge, Information and Creativity Support Systems, KICSS 2012, IEEE , 2012, p. 118-125Conference paper (Refereed)
    Abstract [en]

    As a first step towards developing efficient building energy management techniques, in this paper, we first study the energy consumption patterns of heating, ventilation and cooling (HVAC) systems across the KTH Royal Institute of Technology campus and we identify some possible areas where energy consumption can be made less wasteful. Later, we describe a test-bed where wireless sensor networks are used to collect data and eventually control the HVAC system in a distributed way. We present some of the data, temperature, humidity, and CO2 measurements, that are collected by the aforementioned network and compare them with the measurements collected by the legacy sensors already in place. In the end we present a preliminary result on modelling the dynamics of the temperature, humidity, and CO2 using the data gather by the sensor network. We check the validity of the model via comparing the out put of the system with measured data. As a future work we identify the possibility of using the models obtained here for model based control, and fault detection and isolation techniques.

  • 8. Akesson, M.
    et al.
    Gustafsson, E.
    Johansson, Karl Henrik
    Control design for a helicopter lab process1996Conference paper (Refereed)
  • 9.
    Al Alam, Assad
    et al.
    Scania CV AB.
    Gattami, Ather
    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.
    An experimental study on the fuel reduction potential of heavy duty vehicle platooning2010In: 13th International IEEE Conference on Intelligent Transportation Systems (ITSC), 2010, IEEE , 2010, p. 306-311Conference paper (Refereed)
    Abstract [en]

    Vehicle platooning has become important for the vehicle industry. Yet conclusive results with respect to the fuel reduction possibilities of platooning remain unclear. The focus in this study is the fuel reduction that heavy duty vehicle platooning enables and the analysis with respect to the influence of a commercial adaptive cruise control on the fuel consumption. Experimental results show that by using preview information of the road ahead from the lead vehicle, the adaptive cruise controller can reduce the fuel consumption. A study is undertaken for various masses of the lead vehicle. The results show that the best choice with respect to a heavier or lighter lead vehicle depends on the desired time gap. A maximum fuel reduction of 4.7-7.7% depending on the time gap, at a set speed of 70 km/h, can be obtained with two identical trucks. If the lead vehicle is 10 t lighter a corresponding 3.8-7.4% fuel reduction can be obtained depending on the time gap. Similarly if the lead vehicle is 10 t heavier a 4.3-6.9% fuel reduction can be obtained. All results indicate that a maximum fuel reduction can be achieved at a short relative distance, due to both air drag reduction and suitable control.

  • 10.
    Al Alam, Assad
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Gattami, Ather
    Electrical Engineering and Computer Sciences, UC Berkeley, Berkeley CA, 94720-1770, United States .
    Johansson, Karl Henrik
    Electrical Engineering and Computer Sciences, UC Berkeley, Berkeley CA, 94720-1770, United States .
    Tomlin, Claire Jennifer
    Scania CV AB, Södertälje, Sweden.
    Establishing safety for heavy duty vehicle platooning: a game theoretical approach2011In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2011, p. 3818-3823Conference paper (Refereed)
    Abstract [en]

    It is fuel efficient to minimize the relative distance between vehicles to achievea maximum reduction in air drag. However, the relative distance can only be reduced to acertain extent without endangering a collision. Factors such as the vehicle velocity, the relativevelocity, and the characteristics of the vehicle ahead has a strong impact on what minimumrelative distance can be obtained. In this paper, we utilize optimal control and game theory toestablish safety criteria for heavy duty vehicle platooning applications. The derived results showthat a minimum relative distance of 1.2m can be obtained for two identical vehicles withoutendangering a collision, assuming that there is no delay present in the feedback system. If aworst case delay is present in the system, a minimum relative distance is deduced based uponthe vehicle’s maximum deceleration ability. The relative distance can be reduced if the followervehicle has a greater overall braking capability, which suggests that vehicle heterogeneity andorder has substantial impact. The findings are verified by simulations and the main conclusion isthat the relative distance utilized in commercial applications today can be reduced significantlywith a suitable advanced cruise control system.

  • 11. Alam, Assad
    et al.
    Besselink, Bart
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Turri, Valerio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mårtensson, Jonas
    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.
    Heavy-Duty Vehicle Platooning for Sustainable Freight Transportation A COOPERATIVE METHOD TO ENHANCE SAFETY AND EFFICIENCY2015In: IEEE CONTROL SYSTEMS MAGAZINE, ISSN 1066-033X, Vol. 35, no 6, p. 34-56Article in journal (Refereed)
    Abstract [en]

    The current system of global trade is largely based on transportation and communication technology from the 20th century. Advances in technology have led to an increasingly interconnected global market and reduced the costs of moving goods, people, and technology around the world [1]. Transportation is crucial to society, and the demand for transportation is strongly linked to economic development. Specifically, road transportation is essential since about 60% of all surface freight transportation (which includes road and rail transport) is done on roads [2]. Despite the important role of road freight transportation in the economy, it is facing serious challenges, such as those posed by increasing fuel prices and the need to reduce greenhouse gas emissions. On the other hand, the integration of information and communication technologies to transportation systems-leading to intelligent transportation systems-enables the development of cooperative methods to enhance the safety and energy efficiency of transportation networks. This article focuses on one such cooperative approach, which is known as platooning. The formation of a group of heavy-duty vehicles (HDVs) at close intervehicular distances, known as a platoon (see Figure 1) increases the fuel efficiency of the group by reducing the overall air drag. The safe operation of such platoons requires the automatic control of the velocity of the platoon vehicles as well as their intervehicular distance. Existing work on platooning has focused on the design of controllers for these longitudinal dynamics, in which simple vehicle models are typically exploited and perfect environmental conditions, such as flat roads, are generally assumed. The broader perspective of how platooning can be effectively exploited in a freight transportation system has received less attention. Moreover, experimental validations of the fuel-saving potential offered by platooning have typically been performed by reproducing the perfect conditions as assumed in the design of the automatic controllers. This article focuses on these two aspects by addressing the following two objectives.

  • 12.
    Alam, Assad
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Scania CV AB, SE-15187 Södertälje, Sweden.
    Gattami, Ather
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tomlin, Claire J.
    UC Berkeley.
    Guaranteeing safety for heavy duty vehicle platooning: Safe set computations and experimental evaluations2014In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 24, no 1, p. 33-41Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the problem of finding a safety criteria between neighboring heavy duty vehicles traveling in a platoon. We present a possible framework for analyzing safety aspects of heavy duty vehicle platooning. A nonlinear underlying dynamical model is utilized, where the states of two neighboring vehicles are conveyed through radar information and wireless communication. Numerical safe sets are derived through the framework, under a worst-case scenario, and the minimum safe spacing is studied for heterogenous platoons. Real life experimental results are presented in an attempt to validate the theoretical results in practice. The findings show that a minimum relative distance of 1.2 m at maximum legal velocity on Swedish highways can be maintained for two identical vehicles without endangering a collision. The main conclusion is that the relative distance utilized in commercial applications today can be reduced significantly with a suitable automatic control system.

  • 13. Alam, Assad
    et al.
    Gattami, Ather
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Suboptimal Decentralized Controller Design for Chain Structures: Applications to Vehicle Formations2011In: IEEE 50th Annual Conference on Decision and Control and European Control Conference, Orlando, December, 2011, IEEE , 2011, p. 6894-6900Conference paper (Refereed)
    Abstract [en]

    We consider suboptimal decentralized controllerdesign for subsystems with interconnected dynamics and costfunctions. A systematic design methodology is presented overthe class of linear quadratic regulators (LQR) for chain graphs.The methodology is evaluated on heavy duty vehicle platooningwith physical constraints. A simulation and frequency analysisis performed. The results show that the decentralized controllergives good tracking performance and a robust system. We alsoshow that the design methodology produces a string stablesystem for an arbitrary number of vehicles in the platoon, ifthe vehicle configurations and the LQR weighting parametersare identical for the considered subsystems.

  • 14.
    Alam, Assad
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Experimental evaluation of decentralized cooperative cruise control for heavy-duty vehicle platooning2015In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 38, p. 11-25Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the problem of finding decentralized controllers for heavy-duty vehicle (HDV) platooning by establishing empiric results for a qualitative verification of a control design methodology. We present a linear quadratic control framework for the design of a high-level cooperative platooning controller suitable for modern HDVs. A nonlinear low-level dynamical model is utilized, where realistic response delays in certain modes of operation are considered. The controller performance is evaluated through numerical and experimental studies. It is concluded that the proposed controller behaves well in the sense that experiments show that it allows for short time headways to achieve fuel efficiency, without compromising safety. Simulation results indicate that the model mimics real life behavior. Experiment results show that the dynamic behavior of the platooning vehicles depends strongly on the gear switching logic, which is confirmed by the simulation model. Both simulation and experiment results show that the third vehicle never displays a bigger undershoot than its preceding vehicle. The spacing errors stay bounded within 6.8. m in the simulation results and 7.2. m in the experiment results for varying transient responses. Furthermore, a minimum spacing of -0.6. m and -1.9. m during braking is observed in simulations and experiments, respectively. The results indicate that HDV platooning can be conducted at close spacings with standardized sensors and control units that are already present on commercial HDVs today.

  • 15.
    Alam, Assad
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Look-Ahead Cruise Control for Heavy Duty Vehicle Platooning2013In: Proceedings of the 16th International IEEE Annual Conference onIntelligent Transportation Systems (ITSC 2013), IEEE conference proceedings, 2013, p. 928-935Conference paper (Refereed)
    Abstract [en]

    Vehicle platooning has become important for thevehicle industry. Yet conclusive results with respect to thefuel reduction possibilities of platooning remain unclear, inparticular when considering constraints imposed by the topography.The focus of this study is to establish whether itis more fuel-efficient to maintain or to split a platoon that isfacing steep uphill and downhill segments. Two commercialcontrollers, an adaptive cruise controller and a look-aheadcruise controller, are evaluated and alternative novel controlstrategies are proposed. The results show that an improvedfuel-efficiency can be obtained by maintaining the platoonthroughout a hill. Hence, a cooperative control strategy basedon preview information is presented, which initiates the changein velocity at a specific point in the road for all vehiclesrather than simultaneously changing the velocity to maintainthe spacing. A fuel reduction of up to 14% can be obtainedover a steep downhill segment and a more subtle benefit of0.7% improvement over an uphill segment with the proposedcontroller, compared to the combination of the commerciallyavailable cruise controller and adaptive cruise controller thatcould be used for platooning. The findings show that it isboth fuel-efficient and desirable in practice to consider previewinformation of the topography in the control strategy.

  • 16. Alexandre, Seuret
    et al.
    Dimarogonas, Dimos V.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Consensus of Double Integrator Multi-agents under Communication Delay2009In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2009, p. 376-381Conference paper (Refereed)
    Abstract [en]

    This paper deals with the consensus problem under network induced communication delays. It is well-known that introducing a delay generally leads to a reduce of the performance or to instability. Thus, investigating the impact of time-delays in the consensus problem is an important issue. Another important issue is to obtain an estimate of the convergence rate, which is not straightforward when delays appear in the network. In this paper, the agents are modelled as double integrator systems. It is assumed that each agent receives instantaneously its own output information but receives the information from its neighbors after a constant delay. A stability criterion is provided based on Lyapunov-Krasovskii techniques and is expressed in terms of LMI. An expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The results are supported through several simulations for different network symmetric communication schemes.

  • 17.
    Altaf, Faisal
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Araujo, José
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hernandez, Aitor
    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.
    Wireless event-triggered controller for a 3D tower crane lab process2011In: 2011 19th Mediterranean Conference on Control and Automation, MED 2011, 2011, p. 994-1001Conference paper (Refereed)
    Abstract [en]

    This paper studies the design and real-time implementation of an event-triggered controller for a nonlinear 3D tower crane where the communication between the controller and the actuators is performed over a low-power wireless network. A flexible Event-Generation Circuit (EGC) is proposed in order to implement event-driven controllers for Networked Control Systems. Furthermore, a detailed experimental analysis on the performance of the event-triggered controller and the influence of packet losses on the transmitted actuation messages are presented. The results show that the event-triggered controllers in networked control systems are able to maintain the same level of performance as compared to periodic controllers, while increasing the sensors/actuators lifetime by reducing network bandwidth utilization.

  • 18.
    Altafini, Claudio
    et al.
    SISSA-ISAS International School for Advanced Studies.
    Speranzon, Alberto
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Johansson, Karl Henrik
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Hybrid control of a truck and trailer vehicle2002In: Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349, Vol. 2289, p. 21-34Article in journal (Other academic)
    Abstract [en]

    A hybrid control scheme is proposed for the stabilization of backward driving along simple paths for a miniature vehicle composed of a truck and a two-axle trailer. When reversing, the truck and trailer can be modelled as an unstable nonlinear system with state and input saturations. Due to these constraints the system is impossible to globally stabilize with standard smooth control techniques, since some initial states necessarily lead to that the so called jack-knife locks between the truck and the trailer. The proposed hybrid control method, which combines backward and forward motions, provide a global attractor to the desired reference trajectory. The scheme has been implemented and successfully evaluated on a radio-controlled vehicle. Results from experimental trials are reported.

  • 19. Alur, R.
    et al.
    D'Innocenzo, A.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pappas, G. J.
    Weiss, G.
    Modeling and analysis of multi-hop control networks: RTAS 2009, Proceedings2009In: 15TH IEEE REAL-TIME AND EMBEDDED TECHNOLOGY AND APPLICATION SYMPOSIUM: RTAS 2009, Proceedings, IEEE Computer Society, 2009, p. 223-232Conference paper (Refereed)
    Abstract [en]

    We propose a mathematical framework, inspired by the WirelessHART specification, for modeling and analysing multi-hop communication networks. The framework is designed for systems consisting of multiple control loops closed over a multi-hop communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system. The main technical contribution of the paper is an explicit translation of multi-hop control networks to switched systems. We describe a Mathematica notebook that automates the translation of multihop control networks to switched systems, and use this tool to show how techniques for analysis of switched systems can be used to address control and networking co-design challenges.

  • 20. Alur, Rajeev
    et al.
    D'Innocenzo, Alessandro
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pappas, George J.
    Weiss, Gera
    Compositional Modeling and Analysis of Multi-Hop Control Networks2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 10, p. 2345-2357Article in journal (Refereed)
    Abstract [en]

    We propose a mathematical framework for modeling and analyzing multi-hop control networks designed for systems consisting of multiple control loops closed over a multi-hop (wireless) communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system, providing an explicit translation of multi-hop control networks to switched systems. We propose formal models for analyzing robustness of multi-hop control networks, where data is exchanged through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors, we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability in presence of transient link failures, and give efficient decision procedures. We deal with errors that have random time span and show that, under some conditions, the permanent failure model can be used as a reliable abstraction. Our approach is compositional, namely it addresses the problem of designing scalable scheduling and routing policies for multiple control loops closed on the same multi-hop control network. We describe how the translation of multi-hop control networks to switched systems can be automated, and use it to solve control and networking co-design challenges in some representative examples, and to propose a scheduling solution in a mineral floatation control problem that can be implemented on a time triggered communication protocols for wireless networks.

  • 21.
    Aminian, Behdad
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Araújo, José
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    GISOO: A virtual testbed for wireless cyber-physical systems2013In: Industrial Electronics Society, IECON 2013 - 39th Annual Conference of the IEEE, IEEE , 2013, p. 5588-5593Conference paper (Refereed)
    Abstract [en]

    The increasing demand for wireless cyber-physical systems requires correct design, implementation and validation of computation, communication and control methods. Traditional simulation tools, which focus on either computation, communication or control, are insufficient when the three aspects interact. Efforts to extend the traditional tools to cover multiple domains, e.g., from simulating only control aspects to simulating both control and communication, often rely on simplistic models of a small subset of possible communication solutions. We introduce GISOO, a virtual testbed for simulation of wireless cyber-physical systems that integrates two state-of-the art simulators, Simulink and COOJA. GISOO enables users to evaluate actual embedded code for the wireless nodes in realistic cyber-physical experiments, observing the effects of both the control and communication components. In this way, a wide range of communication solutions can be evaluated without developing abstract models of their control-relevant aspects, and changes made to the networking code in simulations is guaranteed to be translated into production code without errors. A double-tank laboratory experimental setup controlled over a multi-hop relay wireless network is used to validate GISOO and demonstrate its features.

  • 22. Andersson, G.
    et al.
    Esfahani, P. M.
    Vrakopoulou, M.
    Margellos, K.
    Lygeros, J.
    Teixeira, André
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Dán, György
    KTH, School of Electrical Engineering (EES), Communication Networks.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Cyber-security of SCADA systems2012In: 2012 IEEE PES Innovative Smart Grid Technologies, ISGT 2012, IEEE , 2012, p. 6175543-Conference paper (Refereed)
    Abstract [en]

    After a general introduction of the VIKING EU FP7 project two specific cyber-attack mechanisms, which have been analyzed in the VIKING project, will be discussed in more detail. Firstly an attack and its consequences on the Automatic Generation Control (AGC) in a power system are investigated, and secondly the cyber security of State Estimators in SCADA systems is scrutinized.

  • 23.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Amin, Saurabh
    TRUST Center, University of California, Berkeley.
    Schwartz, Galina
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Sastry, Shankar
    TRUST Center, University of California, Berkeley.
    Correlated Failures of Power Systems: Analysis of the Nordic Grid2011In: Preprints of Workshop on Foundations of Dependable and Secure Cyber-Physical Systems, 2011Conference paper (Refereed)
    Abstract [en]

    In this work we have analyzed the effectsof correlated failures of power lines on the total systemload shed. The total system load shed is determined bysolving the optimal load shedding problem, which is thesystem operator’s best response to a system failure.We haveintroduced a Monte Carlo based simulation framework forestimating the statistics of the system load shed as a functionof stochastic network parameters, and provide explicitguarantees on the sampling accuracy. This framework hasbeen applied to a 470 bus model of the Nordic power systemand a correlated Bernoulli failure model. It has been foundthat increased correlations between Bernoulli failures ofpower lines can dramatically increase the expected valueas well as the variance of the system load shed.

  • 24.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Undamped Nonlinear Consensus Using Integral Lyapunov Functions2012In: 2012 American Control Conference (ACC), IEEE Computer Society, 2012, p. 6644-6649Conference paper (Refereed)
    Abstract [en]

    This paper analyzes a class of nonlinear consensus algorithms where the input of an agent can be decoupled into a product of a gain function of the agents own state, and a sum of interaction functions of the relative states of its neighbors. We prove the stability of the protocol for both single and double integrator dynamics using novel Lyapunov functions, and provide explicit formulas for the consensus points. The results are demonstrated through simulations of a realistic example within the framework of our proposed consensus algorithm.

  • 25.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Distributed vs. centralized power systems frequency control2013In: 2013 European Control Conference, ECC 2013, 2013, p. 3524-3529Conference paper (Refereed)
    Abstract [en]

    This paper considers a distributed control algorithm for frequency control of electrical power systems. We propose a distributed controller which retains the reference frequency of the buses under unknown load changes, while asymptotically minimizing a quadratic cost of power generation. For comparison, we also propose a centralized controller which also retains the reference frequency while minimizing the same cost of power generation. We derive sufficient stability criteria for the parameters of both controllers. The controllers are evaluated by simulation on the IEEE 30 bus test network, where their performance is compared.

  • 26.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Control of MTDC Transmission Systems under Local Information2014In: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, p. 1335-1340Conference paper (Refereed)
    Abstract [en]

    High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper a distributed controller for multi-terminal high-voltage direct current (MTDC) transmission systems is considered. Sufficient conditions for when the proposed controller renders the closed-loop system asymptotically stable are provided. Provided that the closed loop system is asymptotically stable, it is shown that in steady-state a weighted average of the deviations from the nominal voltages is zero. Furthermore, a quadratic cost of the current injections is minimized asymptotically.

  • 27.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed controllers for multiterminal HVDC transmission systems2017In: IEEE Transactions on Control of Network Systems, ISSN 2325-5870, Vol. 4, no 3, p. 564-574Article in journal (Refereed)
    Abstract [en]

    High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper the voltagedroop method (VDM) is reviewed, and three novel distributed controllers for multi-terminal HVDC (MTDC) transmission systems are proposed. Sufficient conditions for when the proposed controllers render the closed-loop system asymptotically stable are provided. These conditions give insight into suitable controller architecture, e.g., that the communication graph should be identical with the graph of the MTDC system, including edge weights. Provided that the closed-loop systems are asymptotically stable, it is shown that the voltages asymptotically converge to within predefined bounds. Furthermore, a quadratic cost of the injected currents is asymptotically minimized. The proposed controllers are evaluated on a four-bus MTDC system.

  • 28.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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 H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed PI-Control with Applications to Power Systems Frequency Control2014In: American Control Conference (ACC), 2014, IEEE conference proceedings, 2014, p. 3183-3188Conference paper (Refereed)
    Abstract [en]

    This paper considers a distributed PI-controller for networked dynamical systems. Sufficient conditions for when the controller is able to stabilize a general linear system and eliminate static control errors are presented. The proposed controller is applied to frequency control of power transmission systems. Sufficient stability criteria are derived, and it is shown that the controller parameters can always be chosen so that the frequencies in the closed loop converge to nominal operational frequency. We show that the load sharing property of the generators is maintained, i.e., the input power of the generators is proportional to a controller parameter. The controller is evaluated by simulation on the IEEE 30 bus test network, where its effectiveness is demonstrated.

  • 29.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Distributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 7, p. 1750-1764Article in journal (Refereed)
    Abstract [en]

    This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.

  • 30.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Nazari, Mohammad
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Ghandhari, Mehrdad
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Distributed Voltage and Current Control of Multi-Terminal High-Voltage Direct Current Transmission Systems2014In: Proceedings of the 19th IFAC World Congress, 2014, IFAC Papers Online, 2014, Vol. 19, p. 11910-11916Conference paper (Refereed)
    Abstract [en]

    High-voltage direct current (HVDC) is a commonly used technology for long-distance power transmission, due to its low resistive losses and low costs. In this paper, a novel distributed controller for multi-terminal HVDC (MTDC) systems is proposed. Under certain conditions on the controller gains, it is shown to stabilize the MTDC system. The controller is shown to always keep the voltages close to the nominal voltage, while assuring that the injected power is shared fairly among the converters. The theoretical results are validated by simulations, where the affect of communication time-delays is also studied.

  • 31.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Dimarogonas, Dimos V.
    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.
    Distributed integral action: stability analysis and frequency control of power systems2012In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, p. 2077-2083Conference paper (Refereed)
    Abstract [en]

    This paper analyzes distributed proportional-integral controllers. We prove that integral action can be successfully applied to consensus algorithms, where attenuation of static disturbances is achieved. These control algorithms are applied to decentralized frequency control of electrical power systems. We show that the proposed algorithm can attenuate step disturbances of power loads. We provide simulations of the proposed control algorithm on the IEEE 30 bus test system that demonstrate its efficiency.

  • 32.
    Andreasson, Martin
    et al.
    KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sjödin, Emma
    KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Industrial Engineering and Management (ITM). KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Coherence in Synchronizing Power Networks with Distributed Integral Control2017In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, p. 6683-6688Conference paper (Refereed)
    Abstract [en]

    We consider frequency control of synchronous generator networks and study transient performance under both primary and secondary frequency control. We model random step changes in power loads and evaluate performance in terms of expected deviations from a synchronous frequency over the synchronization transient; what can be thought of as lack of frequency coherence. We compare a standard droop control strategy to two secondary proportional integral (PI) controllers: centralized averaging PI control (CAPI) and distributed averaging PI control (DAPI). We show that the performance of a power system with DAPI control is always superior to that of a CAPI controlled system, which in turn has the same transient performance as standard droop control. Furthermore, for a large class of network graphs, performance scales unfavorably with network size with CAPI and droop control, which is not the case with DAPI control. We discuss optimal tuning of the DAPI controller and describe how internodal alignment of the integral states affects performance. Our results are demonstrated through simulations of the Nordic power grid.

  • 33.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tegling, Emma
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH Royal Inst Technol, Sch Elect Engn, SE-10044 Stockholm, Sweden.;KTH Royal Inst Technol, ACCESS Linnaeus Ctr, SE-10044 Stockholm, Sweden..
    Performance and Scalability of Voltage Controllers in Multi-Terminal HVDC Networks2017In: 2017 AMERICAN CONTROL CONFERENCE (ACC), IEEE , 2017, p. 3029-3034Conference paper (Refereed)
    Abstract [en]

    In this paper, we compare the transient performance of a multi-terminal high-voltage DC (MTDC) grid equipped with a slack bus for voltage control to that of two distributed control schemes: a standard droop controller and a distributed averaging proportional-integral (DAPI) controller. We evaluate performance in terms of an H-2 metric that quantifies expected deviations from nominal voltages, and show that the transient performance of a droop or DAPI controlled MTDC grid is always superior to that of an MTDC grid with a slack bus. In particular, by studying systems built up over lattice networks, we show that the H-2 norm of a slack bus controlled system may scale unboundedly with network size, while the norm remains uniformly bounded with droop or DAPI control. We simulate the control strategies on radial MTDC networks to demonstrate that the transient performance for the slack bus controlled system deteriorates significantly as the network grows, which is not the case with the distributed control strategies.

  • 34.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wiget, R.
    Dimarogonas, Dimos
    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.
    Andersson, G.
    Coordinated frequency control through MTDC transmission systems2015In: IFAC Proceedings, Elsevier, 2015, Vol. 48, no 22, p. 106-111Conference paper (Refereed)
    Abstract [en]

    In this paper we propose a distributed dynamic controller for sharing frequency control reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions, which guarantee that the frequencies of the AC systems converge to the nominal frequency. Simultaneously, the global quadratic cost of power generation is minimized, resulting in an optimal distribution of generation control reserves. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal voltages. The proposed controller is tested on a high-order dynamic model of a power system consisting of asynchronous AC grids, modelled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation.

  • 35.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wiget, R.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, G.
    Distributed Frequency Control Through MTDC Transmission Systems2017In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 32, no 1, p. 250-260, article id 7456314Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose distributed dynamic controllers for sharing both frequency containment and restoration reserves of asynchronous ac systems connected through a multi-terminal HVDC (MTDC) grid. The communication structure of the controller is distributed in the sense that only local and neighboring state information is needed, rather than the complete state. We derive sufficient stability conditions, which guarantee that the ac frequencies converge to the nominal frequency. Simultaneously, a global quadratic power generation cost function is minimized. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal dc voltages. The results are valid for distributed cable models of the HVDC grid (e.g., $\pi$-links), as well as ac systems of arbitrary number of synchronous machines, each modeled by the swing equation. We also propose a decentralized communication-free version of the controller. The proposed controllers are tested on a high-order dynamic model of a power system consisting of asynchronous ac grids, modeled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation. © 1969-2012 IEEE.

  • 36.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wiget, Roger
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Andersson, Goran
    Distributed Secondary Frequency Control through MTDC Transmission Systems2015In: 2015 54TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 2627-2634Conference paper (Refereed)
    Abstract [en]

    In this paper, we present distributed controllers for sharing primary and secondary frequency control reserves for asynchronous AC transmission systems, which are connected through a multi-terminal HVDC grid. By using Lyapunov arguments, the equilibria of the closed-loop system are shown to be globally asymptotically stable. We quantify the static errors of the voltages and frequencies, and give upper bounds for these errors. It is also shown that the controllers have the property of power sharing, i.e., primary and secondary frequency control reserves are shared fairly amongst the AC systems. The proposed controllers are applied to a high-order dynamic model of of a power system consisting of asynchronous AC grids connected through a six-terminal HVDC grid.

  • 37.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wiget, Roger
    ETH Zurich.
    Dimarogonas, Dimos V
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Andersson, Göran
    ETH Zurich.
    Distributed Primary Frequency Control through Multi-Terminal HVDC Transmission Systems2015In: American Control Conference (ACC), 2015, IEEE conference proceedings, 2015, p. 5029-5034Conference paper (Refereed)
    Abstract [en]

    This paper presents a decentralized controller for sharing primary AC frequency control reserves through a multi-terminal HVDC grid. By using passivity arguments, the proposed controller is shown to stabilize the closed-loop system consisting of the interconnected AC and HVDC grids, given any positive controller gains. The static control errors resulting from the proportional controller are quantified and bounded by analyzing the equilibrium of the closed-loop system. The proposed controller is applied to a test grid consisting of three asynchronous AC areas interconnected by an HVDC grid, and its effectiveness is validated through simulation.

  • 38.
    Andreasson, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Wiget, Roger
    Power Systems Laboratory,Switzerland.
    Dimarogonas, Dimos V
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Andersson, Göran
    Power Systems Laboratory,Switzerland.
    Distributed Secondary Frequency Control through Multi-Terminal HVDC Transmission Systems2015In: Decision and Control (CDC), 2015 IEEE 54th Annual Conference on, IEEE conference proceedings, 2015, p. 2627-2634Conference paper (Refereed)
    Abstract [en]

    In this paper, we present distributed controllers for sharing primary and secondary frequency control reserves for asynchronous AC transmission systems, which are connected through a multi-terminal HVDC grid. By using passivity arguments, the equilibria of the closed-loop system are shown to be globally asymptotically stable. We quantify the static errors of the voltages and frequencies, and give upper bounds for these errors. It is also shown that the controllers have the property of power sharing, i.e., primary and secondary frequency control reserves are shared fairly amongst the AC systems. The proposed controllers are applied to a high-order dynamic model of of a power system consisting of asynchronous AC grids connected through a 6-terminal HVDC grid.

  • 39. Aragues, R.
    et al.
    Shi, Guodong
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sagues, C.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed algebraic connectivity estimation for adaptive event-triggered consensus2012In: American Control Conference (ACC), 2012, IEEE , 2012, p. 32-37Conference paper (Refereed)
    Abstract [en]

    In several multi agent control problems, the convergence properties and speed of the system depend on the algebraic connectivity of the graph. We discuss a particular event-triggered consensus scenario, and show that the availability of an estimate of the algebraic connectivity could be used for adapting the behavior of the average consensus algorithm. We present a novel distributed algorithm for estimating the algebraic connectivity, that relies on the distributed computation of the powers of matrices. We provide proofs of convergence, convergence rate, and upper and lower bounds at each iteration of the estimated algebraic connectivity.

  • 40. Aragues, Rosario
    et al.
    Shi, Guodong
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Saguees, Carlos
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mezouar, Youcef
    Distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 12, p. 3253-3259Article in journal (Refereed)
    Abstract [en]

    The algebraic connectivity of the graph Laplacian plays an essential role in various multi-agent control systems. In many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance. Lately, several methods based on distributed Power Iteration have been proposed for computing the algebraic connectivity of a symmetric Laplacian matrix. However, these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear. In this paper, we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric Laplacian matrices. Our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that, at each iteration, agents obtain both upper and lower bounds for the true algebraic connectivity. Both bounds successively approach the true algebraic connectivity with the convergence speed no slower than O(1/k).

  • 41.
    Araujo, Jose
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ariba, Yassine
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Park, Pangun
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Control over a Hybrid MAC Wireless Network2010In: 2010 IEEE 1ST INTERNATIONAL CONFERENCE ON SMART GRID COMMUNICATIONS, 2010, p. 197-202Conference paper (Refereed)
    Abstract [en]

    Wireless Sensor Networks and Control Systems are an essential part of the Smart Grid. We consider the problem of performing control over large complex networked systems with packet drops. More specifically, we are interested in improving the performance of the regulation of control loops when the communication is made over low-cost wireless networks. In control over wireless networks it is common to use Contention-Free (CF) schemes where no losses occur with the price of low scalability and complicated scheduling policies. In this work we propose a hybrid MAC and control architecture, where a small number of control loops with high demand of attention are scheduled in a CF scheme and well regulated loops are scheduled in a lossy, asynchronous and highly scalable, Contention-Access (CA) scheme. We model and analyze the performance of such system with Markov Jump Linear System (MJLS) tools and compare it with other architecture types. Performance is evaluated using a quadratic cost function of the state.

  • 42.
    Araujo, Jose
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Fawzi, Hamza
    Department of Electrical Engineering, University of California Los Angeles, USA.
    Mazo Jr., Manuel
    INCAS 3 & University of Groningen, The Netherlands.
    Tabuada, Paulo
    Department of Electrical Engineering, University of California Los Angeles, USA.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    An improved self-triggered implementation for linear controllers2012Conference paper (Refereed)
    Abstract [en]

    Research in networked control systems raised the importance of understanding what are thetiming requirements for control. In recent years this problem has been attacked from multiple anglesincluding the computation of Maximal Allowable Transmission Intervals, event-triggered, and selftriggered controller implementations. In a self-triggered implementation the controller is responsible forcomputing the next time instant at which the actuator values should be updated by evaluating the controllaw on fresh sensor measurements. One of the main challenges in self-triggered control is how to performthe exact calculation of the time at which these updates should take place. In this paper we present anew technique to compute lower bounds on the self-triggered update times in a computationally lightmanner. We evaluate the algorithm on numerical examples and we observe that the algorithm performswell when compared to other existing methods and provides tight lower bounds on the exact updatetimes. Additionally, we propose a Semidefinite Programming-based technique that produces triggeringconditions that are less conservative than the existing ones and for which the update times are larger.

  • 43.
    Araujo, Jose
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Experimental Validation of a Localization System Based on a Heterogeneous Sensor Network2009In: ASCC: 2009 7TH ASIAN CONTROL CONFERENCE, NEW YORK: IEEE , 2009, p. 465-470Conference paper (Refereed)
    Abstract [en]

    The experimental implementation and validation of a localization system based on a heterogeneous sensor network is described. The sensor network consists of ultrasound ranging sensors and web cameras. They are used to localize a mobile robot under sensor communication constraints. Applying a recently proposed sensor fusion algorithm that explicitly takes communication delay and cost into account, it is shown that one can accurately trade off the estimation performance by using low-quality ultrasound sensors with low processing time and low communication cost versus the use of the high-quality cameras with longer processing time and higher communication cost. It is shown that a periodic schedule of the sensors is suitable in many cases. The experimental setup is discussed in detail and experimental results are presented.

  • 44.
    Araujo, José
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Anta, A.
    Mazo Jr., M.
    Faria, Jo˜ao
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hernandez, Aitor
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tabuda, P.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Self-triggered control for industrial wireless sensor and actuator networks2011Conference paper (Refereed)
    Abstract [en]

    Energy and communication bandwidth are scarceresources in wireless sensor and actuator networks. Recentresearch efforts considered the control of physical processes oversuch resource limited networks. Most of the existing literatureaddressing this topic is dedicated to periodically sampled controlloops and scheduled communication, because it simplifies theanalysis and the implementation. We propose instead an aperiodicnetwork transmission scheme that reduces the number oftransmission instances for the sensor and control nodes, therebyreducing energy consumption and increasing network lifetime,without sacrificing control performance. As an added benefit,we show the possibility of dynamically allocating the networkbandwidth based on the physical system state and the availableresources. In order to allow timely, reliable, and energy efficientcommunication, we propose a new co-design framework forthe wireless medium access control, compatible with the IEEE802.15.4 standard. Furthermore, we validate our approach in areal wireless networked control implementation.

  • 45.
    Araújo, José
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Anta, A.
    Mazo Jr., M.
    Faria, J.
    Hernandez, Aitor
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Tabuada, P.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Self-triggered control over wireless sensor and actuator networks2011Conference paper (Refereed)
    Abstract [en]

    Energy and communication bandwidth are scarce resources in wireless sensor and actuator networks. Recent research efforts considered the control of physical processes over such resource limited networks. Most of the existing literature addressing this topic is dedicated to periodically sampled control loops and scheduled communication, because it simplifies the analysis and the implementation. We propose instead an aperiodic network transmission scheme that reduces the number of transmission instances for the sensor and control nodes, thereby reducing energy consumption and increasing network lifetime, without sacrificing control performance. As an added benefit, we show the possibility of dynamically allocating the network bandwidth based on the physical system state and the available resources. In order to allow timely, reliable, and energy efficient communication, we propose a new co-design framework for the wireless medium access control, compatible with the IEEE 802.15.4 standard. Furthermore, we validate our approach in a real wireless networked control implementation.

  • 46.
    Araújo, José
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mazo, M.
    Anta, A.
    Tabuada, P.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    System architectures, protocols and algorithms for aperiodic wireless control systems2014In: IEEE Transactions on Industrial Informatics, ISSN 1551-3203, E-ISSN 1941-0050, Vol. 10, no 1, p. 175-184Article in journal (Refereed)
    Abstract [en]

    Wide deployment of wireless sensor and actuator networks in cyber-physical systems requires systematic design tools to enable dynamic tradeoff of network resources and control performance. In this paper, we consider three recently proposed aperiodic control algorithms which have the potential to address this problem. By showing how these controllers can be implemented over the IEEE 802.15.4 standard, a practical wireless control system architecture with guaranteed closed-loop performance is detailed. Event-based predictive and hybrid sensor and actuator communication schemes are compared with respect to their capabilities and implementation complexity. A two double-tank laboratory experimental setup, mimicking some typical industrial process control loops, is used to demonstrate the applicability of the proposed approach. Experimental results show how the sensor communication adapts to the changing demands of the control loops and the network resources, allowing for lower energy consumption and efficient bandwidth utilization.

  • 47.
    Araújo, José
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Teixeira, André
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Henriksson, Erik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    A down-sampled controller to reduce network usage with guaranteed closed-loop performance2014In: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, p. 6849-6856Conference paper (Refereed)
    Abstract [en]

    We propose and evaluate a down-sampled controller which reduces the network usage while providing a guaranteed desired linear quadratic control performance. This method is based on fast and slow sampling intervals, as the closed-system benefits by being brought quickly to steady-state conditions while behaving satisfactorily when being actuated at a slow rate once at those conditions. This mechanism is shown to provide large savings with respect to network usage when compared to traditional periodic time-triggered control and other aperiodic controllers proposed in the literature.

  • 48.
    Ares, Benigno Zurita
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Fischione, Carlo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Energy consumption of minimum energy coding in CDMA wireless sensor networks2007In: Wireless Sensor Networks / [ed] Langendoen, K; Voigt, T, Springer Berlin/Heidelberg, 2007, Vol. 4373, p. 212-227Conference paper (Other academic)
    Abstract [en]

    A theoretical framework is proposed for accurate performance analysis of minimum energy coding schemes in Coded Division Multiple Access (CDMA) wireless sensor networks. Bit error rate and average energy consumption is analyzed for two coding schemes proposed in the literature: Minimum Energy coding (ME), and Modified Minimum Energy coding (MME). Since CDMA wireless systems are strongly limited by multi access interference, the system model includes all the relevant characteristics of the wireless propagation. Furthermore, a detailed model of the energy consumption is described as function of the coding schemes, the radio transmit powers, the characteristics of the transceivers, and the dynamics of the wireless channel. A distributed radio power minimization algorithm is also addressed. Numerical results show that ME and MME coding schemes exhibit similar bit error probabilities, whereas MME outperforms ME only in the case of low data rate and large coding codewords.

  • 49. Ariba, Y.
    et al.
    Briat, C.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Simple conditions for $L_2$ stability and stabilization of networked control systems2011In: Proceeding of 8th International Federation of Automatic Control (IFAC) World Congress, 2011, p. 96-101Conference paper (Refereed)
    Abstract [en]

    The stability analysis and stabilization of networked control systems subject todata loss and time-varying transmission delays are explored. The stability result is based onquadratic separation and operator theory, which allows to capture the above phenomena intothe single formalism of aperiodic sampling. The obtained stability condition is expressed throughan LMI. The stabilization problem is a bit more involved due to the inherent structure of theobtained LMI. An approximation (dilation) is then proposed to obtain a more tractable LMIfor stabilization. Several examples illustrate the effectiveness of the proposed approach.

  • 50.
    Ariba, Yassine
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gouaisbaut, F.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Stability interval for time-varying delay systems2010Conference paper (Refereed)
    Abstract [en]

    We investigate the stability analysis of linear time-delay systems. The time-delay is assumed to be a time-varying continuous function belonging to an interval (possibly excluding zero) with a bound on its derivative. To this end, we propose to use the quadratic separation framework to assess the intervals on the delay that preserves the stability. Nevertheless, to take the time-varying nature of the delay into account, the quadratic separation principle has to be extended to cope with the general case of time-varying operators. The key idea lies in rewording the delay system as a feedback interconnection consisting of operators that characterize it. The original feature of this contribution is to design a set of additional auxiliary operators that enhance the system modelling and reduce the conservatism of the methodology. Then, separation conditions lead to linear matrix inequality conditions which can be efficiently solved with available semi-definite programming algorithms. The paper concludes with illustrative academic examples.

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