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  • 1.
    Adaldo, Antonio
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Alderisio, Francesco
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Liuzza, Davide
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    di Bernardo, Mario
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Event-triggered pinning control of complex networks with switching topologies2014Ingår i: Proceedings of the 53rd annual IEEE Conference on Decision and Control, 2014, s. 2783-2788Konferensbidrag (Refereegranskat)
    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, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Alderisio, Francesco
    Liuzza, Davide
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    di Bernardo, Mario
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. University of Naples Federico II, Italy.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Event-Triggered Pinning Control of Switching Networks2015Ingår i: IEEE Transactions on Control of Network Systems, ISSN 2325-5870, Vol. 2, nr 2, s. 204-213, artikel-id 7098382Artikel i tidskrift (Refereegranskat)
    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. Aragues, R.
    et al.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sagues, C.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Distributed algebraic connectivity estimation for adaptive event-triggered consensus2012Ingår i: American Control Conference (ACC), 2012, IEEE , 2012, s. 32-37Konferensbidrag (Refereegranskat)
    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.

  • 4.
    Lou, Youcheng
    et al.
    Chinese Acad Sci, Beijing, Peoples R China .
    Hong, Yiguang
    Chinese Acad Sci, Beijing, Peoples R China .
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Target aggregation of second-order multi-agent systems with switching interconnection2012Ingår i: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 25, nr 3, s. 430-440Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set spanned by these moving leaders. With the condition on switching interconnection topologies, all mobile agents can asymptotically track the dynamical target set specified by multiple moving leaders with bounded error. Moreover, discussion on the case with static leaders is also given.

  • 5.
    Lou, Youcheng
    et al.
    Chinese Academy of Sciences, Beijing, China .
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Y.
    Convergence of random sleep algorithms for optimal consensus2013Ingår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 62, nr 12, s. 1196-1202Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we propose a random sleep algorithm for a network to cooperatively find a point within the intersection of some convex sets, each of which is known only to a particular node. At each step, each node first chooses to project its own set or not at random by a Bernoulli decision independently. When a node has chosen to project its set, we assume that it can detect only the projection direction rather than the exact projection point, based on which the node obtains an estimate for the projection point. Then the agents update their states by averaging the estimates with their neighbors. Under directed and time-varying communication graph, sufficient and/or necessary stepsize conditions are presented for the considered algorithm converging to a consensus within the intersection set.

  • 6. Lou, Youcheng
    et al.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Yiguang
    Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle2014Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, nr 7, s. 1722-1736Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that pi/4 is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

  • 7. Lou, Youcheng
    et al.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Yiguang
    Reaching optimal consensus for multi-agent systems based on approximate projection2012Ingår i: 10th World Congress on Intelligent Control and Automation (WCICA), 2012, IEEE conference proceedings, 2012, s. 2794-2800Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we propose an approximately projected consensus algorithm (APCA) for a network to cooperatively compute the intersection of several convex sets, each of which is known only to a particular node. Instead of assuming the exact convex projection, we allow each node to just compute an approximate projection. The communication graph is directed and time-varying, and nodes can only exchange information via averaging among local view. We present sufficient and/or necessary conditions for the APCA, which shows on how much projection accuracy is required to ensure a global consensus within the intersection set when the communication graphs is uniformly jointly strongly connected. We show that π/4 is a critical angle error in the projection approximation to ensure a bounded solution for iterative projections. A numerical example indicates that the APCA may achieve better performance than the exact projected consensus algorithm. The results add the understanding of the fundamentals of distributed convex intersection computation.

  • 8.
    Meng, Ziyang
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Multi-agent systems with compasses: Cooperative and cooperative-antagonistic networks2014Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we first study agreement protocols for coupled continuous-time nonlinear dynamics over cooperative multi-agent networks. To guarantee convergence for such systems, it is common in the literature to assume that the vector field of each agent is pointing inside the convex hull formed by the states of the agent and its neighbors given the relative states between each agent and its neighbors are available. This convexity condition is relaxed in this paper, as we show that it is enough that the vector field belongs to a strict tangent cone based on a local supporting hyperrectangle. The new condition has the natural physical interpretation of adding a compass for each agent in addition to the available local relative states, as each agent needs only to know in which orthant each of its neighbor is. It is proven that the multi-agent system achieves exponential state agreement if and only if the time-varying interaction graph is uniformly jointly quasi-strongly connected. Cooperative-antagonistic multi-agent networks are also considered. For these systems, the (cooperative-antagonistic) relation has a negative sign for arcs corresponding to antagonistic interactions. State agreement may not be achieved for cooperative-antagonistic multi-agent systems. Instead it is shown that asymptotic modulus agreement is achieved if the time-varying interaction graph is uniformly jointly strongly connected.

  • 9.
    Meng, Ziyang
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Yang, Tao
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Dimarogonas, Dimos V
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Hong, Yiguang
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Set target aggregation of multiple mechanical systems2014Ingår i: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, nr February, s. 6830-6835Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we study the set target aggregation problem of multiple mechanical systems. Each system is modeled by a Lagrangian dynamical equation and observes a convex set as its local target. The objective of the group is to reach an aggregation towards these target sets.We propose a set target aggregation algorithm that is constructed based on each mechanical system's own target sensing and the exchange of its information with local neighbors. With necessary connectivity for both fixed and switching communication topologies, multiple mechanical systems are shown to converge to the intersection of all the local target sets while the vectors of generalized coordinate derivatives are driven to zero. Simulations are given to validate the theoretical results.

  • 10.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Multi-agent systems reaching optimal consensus with time-varying communication graphs2011Ingår i: IFAC Proceedings Volumes: (IFAC-PapersOnline), 2011, nr PART 1, s. 5693-5699Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, an optimal consensus problem for continuous-time multi-agent systems is formulated and solved with time-varying interconnection topologies. Based on a sharp connectivity assumption, the considered multi-agent network with simple nonlinear distributed control rules achieves not only a consensus, but also an optimal one by agreeing within the global optimal solution set of a sum of objective functions corresponding to multiple agents. Convergence analysis is presented, by establishing several key properties of a class of distance functions and invariant sets with the help of convex analysis and non-smooth analysis.

  • 11.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Yiguang
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Connectivity and set tracking of multi-agent systems guided by multiple moving leaders2012Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, nr 3, s. 663-676Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we investigate distributed multi-agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities. Various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking. Based on the connectivity of the time-varying multi-agent system, necessary and sufficient conditions are obtained for set input-to-state stability and set integral input-to-state stability for a nonlinear neighbor-based coordination rule with switching directed topologies. Conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders.

  • 12.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Agreeing under randomized network dynamics2012Ingår i: 2012 American Control Conference (ACC), IEEE Computer Society, 2012, s. 2394-2400Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we study randomized consensus processing over general random graphs. At time step k, each node will follow the standard consensus algorithm, or stick to current state by a simple Bernoulli trial with success probability pk. Connectivity-independent and arc-independent graphs are defined, respectively, to capture the fundamental independence of random graph processes with respect to a consensus convergence. Sufficient and/or necessary conditions are presented on the success probability sequence for the network to reach a global a.s. consensus under various conditions of the communication graphs. Particularly, for arc-independent graphs with simple self-confidence condition, we show that Σk pk is a sharp threshold corresponding to a consensus 0 1 law, i.e., the consensus probability is 0 for almost all initial conditions if Σk pk converges, and jumps to 1 for all initial conditions if Σk pk diverges.

  • 13.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Convergence of distributed averaging and maximizing algorithms: Part I: Time-dependent graphs2013Ingår i: 2013 American Control Conference (ACC), American Automatic Control Council , 2013, s. 6096-6101Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we formulate and investigate a generalized consensus algorithm which makes an attempt to unify distributed averaging and maximizing algorithms considered in the literature. Each node iteratively updates its state as a time-varying weighted average of its own state, the minimal state, and the maximal state of its neighbors. This part of the paper focuses on time-dependent communication graphs. We prove that finite-time consensus is almost impossible for averaging under this uniform model. Then various necessary and/or sufficient conditions are presented on the consensus convergence. The results characterize some similarities and differences between distributed averaging and maximizing algorithms.

  • 14.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Convergence of Distributed Averaging and Maximizing Algorithms: Part II: State-dependent Graphs2013Ingår i: 2013 American Control Conference, American Automatic Control Council , 2013, s. 6859-6864Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we formulate and investigate a generalized consensus algorithm which makes an attempt to unify distributed averaging and maximizing algorithms considered in the literature. Each node iteratively updates its state as a time-varying weighted average of its own state, the minimal state, and the maximal state of its neighbors. In Part I of the paper, time-dependent graphs are studied. This part of the paper focuses on state-dependent graphs. We use a μ-nearest-neighbor rule, where each node interacts with its μ nearest smaller neighbors and the μ nearest larger neighbors. It is shown that μ+1 is a critical threshold on the total number of nodes for the transit from finite-time to asymptotic convergence for averaging, in the absence of node self-confidence. The threshold is 2μ if each node chooses to connect only to neighbors with unique values. The results characterize some similarities and differences between distributed averaging and maximizing algorithms.

  • 15.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Multi-agent Robust Consensus-Part I: Convergence Analysis2011Ingår i: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC), 2011Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper investigates a robust consensus problemfor continuous-time nonlinear multi-agent systems withtime-varying communication graphs. Convergence rates arepresented explicitly with respect to L1 and L1 norms ofdisturbances. Sufficient and necessary connectivity conditionsare obtained for the system to reach robust consensus orintegral robust consensus.

  • 16.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Multi-agent Robust Consensus-Part II: Application to Event-triggered Coordination2011Ingår i: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC), 2011, s. 5738-5743Konferensbidrag (Refereegranskat)
    Abstract [en]

    In the first part of the paper, robust consensuswas discussed for continuous-time multi-agent systems withuncertainties in the dynamics. As an application of the robustconsensus analysis, this part of the paper further investigatesdistributed multi-agent coordination via event-triggeredstrategies, where the control input of each agent is piecewiseconstant. Each agent chooses the instances to update itscontrol input by checking whether its state error meets a giventime-dependent function or not. Proper triggering conditionsare given for the system to reach a global consensus usingpiecewise costant control with directed time-varying communicationgraphs under neighbor-synchronous and asynchronousupdating protocols, respectively.

  • 17.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Multi-agent systems reaching optimal consensus based on simple Bernoulli decisions2012Ingår i: 31st Chinese Control Conference (CCC), IEEE conference proceedings, 2012, s. 6273-6278Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z∊Rd Σni=1 fi(z), in which the optimal solution set of objective function fi corresponding to agent i can only be observed by agent i itself. At each time step, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. The results illustrate that a group of autonomous agents can reach an optimal opinion with probability one by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step.

  • 18.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Persistent graphs and consensus convergence2012Ingår i: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2012, s. 2046-2051Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper investigates the role persistent arcs play for averaging algorithms to reach a global consensus under discrete-time or continuous-time dynamics. Each (directed) arc in the underlying communication graph is assumed to be associated with a time-dependent weight function. An arc is said to be persistent if its weight function has infinite ℒ1 or ℓ1 norm for continuous-time or discrete-time models, respectively. The graph that consists of all persistent arcs is called the persistent graph of the underlying network. Three necessary and sufficient conditions on agreement or ε-agreement are established, by which we prove that the persistent graph fully determines the convergence to a consensus. It is also shown how the convergence rates explicitly depend on the diameter of the persistent graph.

  • 19.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Randomized optimal consensus of multi-agent systems2012Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, nr 12, s. 3018-3030Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we formulate and solve a randomized optimal consensus problem for multi-agent systems with stochastically time-varying interconnection topology. The considered multi-agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min(z is an element of Rd) Sigma(n)(i=1) f(i)(z), in which the optimal solution set of objective function f(i) can only be observed by agent i itself. At each time step, simply determined by a Bernoulli trial, each agent independently and randomly chooses either taking an average among its neighbor set, or projecting onto the optimal solution set of its own optimization component. Both directed and bidirectional communication graphs are studied. Connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions. The convergence analysis is carried out using convex analysis. We compare the randomized algorithm with the deterministic one via a numerical example. The results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade-off between following its neighbors or sticking to its own opinion at each time step.

  • 20.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Robust Consensus For Continuous-Time Multiagent Dynamics2013Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 51, nr 5, s. 3673-3691Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to L-infinity and L-1 norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions. The results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance. The epsilon-convergence time is obtained for the consensus computation on directed and K-bidirectional graphs.

  • 21.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    The role of persistent graphs in the agreement seeking of social networks2013Ingår i: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 31, nr 9, s. 595-606Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper investigates the role persistent relations play for a social network to reach a global belief agreement under discrete-time or continuous-time evolution. Each directed arc in the underlying communication graph is assumed to be associated with a time-dependent weight function, which describes the strength of the information flow from one node to another. An arc is said to be persistent if its weight function has infinite L1 or l1 norm for continuous or discrete belief evolutions, respectively. The graph that consists of all persistent arcs is called the persistent graph of the underlying network. Three necessary and sufficient conditions on agreement or ε-agreement are established. We prove that the persistent graph fully determines the convergence to a common opinion in a social network. It is shown how the convergence rate explicitly depends on the diameter of the persistent graph. For a social networking service like Facebook, our results indicate how permanent friendships need to be and what network topology they should form for the network to be an efficient platform for opinion diffusion.

  • 22.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Y.
    Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets2013Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, nr 3, s. 610-622Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, multi-agent systems minimizing a sum of objective functions, where each component is only known to a particular node, is considered for continuous-time dynamics with time-varying interconnection topologies. Assuming that each node can observe a convex solution set of its optimization component, and the intersection of all such sets is nonempty, the considered optimization problem is converted to an intersection computation problem. By a simple distributed control rule, the considered multi-agent system with continuous-time dynamics achieves not only a consensus, but also an optimal agreement within the optimal solution set of the overall optimization objective. Directed and bidirectional communications are studied, respectively, and connectivity conditions are given to ensure a global optimal consensus. In this way, the corresponding intersection computation problem is solved by the proposed decentralized continuoustime algorithm. We establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non-smooth analysis.

  • 23.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Hong, Yiguang
    Multi-agent Systems Reaching Optimal Consensus with Directed Communication Graphs2011Ingår i: 2011 AMERICAN CONTROL CONFERENCE, 2011, s. 5456-5461Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we investigate an optimal consensus problem for multi-agent systems with directed interconnection topologies. Based on a nonlinear distributed coordination rule with switching directed communicating graphs, the considered multi-agent system achieves not only a consensus, but also an optimal one by agreeing within the global solution set of a sum of objective functions corresponding to multiple agents. The optimal solution set convergence and consensus analysis are given respectively with the help of convex analysis and nonsmooth analysis.

  • 24.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    How agreement and disagreement evolve over random dynamic networks2013Ingår i: IEEE Journal on Selected Areas in Communications, ISSN 0733-8716, E-ISSN 1558-0008, Vol. 31, nr 6, s. 1061-1071Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of faults in a large-scale control system, or the development of trust and mistrust in a society. At each time instance and with a given probability, a pair of network nodes interact. At random each of the nodes then updates its state towards the state of the other node (attraction), away from the other node (repulsion), or sticks to its current state (neglect). Agreement convergence and disagreement divergence results are obtained for various strengths of the updates for both symmetric and asymmetric update rules. Impossibility theorems show that a specific level of attraction is required for almost sure asymptotic agreement and a specific level of repulsion is required for almost sure asymptotic disagreement. A series of sufficient and/or necessary conditions are then established for agreement convergence or disagreement divergence. In particular, under symmetric updates, a critical convergence measure in the attraction and repulsion update strength is found, in the sense that the asymptotic property of the network state evolution transits from agreement convergence to disagreement divergence when this measure goes from negative to positive. The result can be interpreted as a tight bound on how much bad action needs to be injected in a dynamic network in order to consistently steer its overall behavior away from consensus.

  • 25.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Randomized Gossiping with Unreliable Communication: Dependent or Independent Node Updates2012Ingår i: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2012, s. 4846-4851Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper studies an asynchronous randomized gossip algorithm under unreliable communication. At each instance, two nodes are selected to meet with a given probability. When nodes meet, two unreliable communication links are established with communication in each direction succeeding with a time-varying probability. It is shown that two particularly interesting cases arise when these communication processes are either perfectly dependent or independent. Necessary and sufficient conditions on the success probability sequence are proposed to ensure almost sure consensus or ?-consensus. Weak connectivity is required when the communication is perfectly dependent, while double connectivity is required when the communication is independent. Moreover, it is proven that with odd number of nodes, average preserving turns from almost forever (with probability one for all initial conditions) for perfectly dependent communication, to almost never (with probability zero for almost all initial conditions) for the independent case. This average preserving property does not hold true for general number of nodes. These results indicate the fundamental role the node interactions have in randomized gossip algorithms.

  • 26.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Proutiere, Alexandre
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Mikael
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Randomized consensus with attractive and repulsive links2013Ingår i: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2013, s. 2599-2604Konferensbidrag (Refereegranskat)
    Abstract [en]

    We study convergence properties of a randomized consensus algorithm over a graph with both attractive and repulsive links. At each time instant, a node is randomly selected to interact with a random neighbor. Depending on if the link between the two nodes belongs to a given subgraph of attractive or repulsive links, the node update follows a standard attractive weighted average or a repulsive weighted average, respectively. The repulsive update has the opposite sign of the standard consensus update. In this way, it counteracts the consensus formation and can be seen as a model of link faults or malicious attacks in a communication network, or the impact of trust and antagonism in a social network. Various probabilistic convergence and divergence conditions are established. A threshold condition for the strength of the repulsive action is given for convergence in expectation: when the repulsive weight crosses this threshold value, the algorithm transits from convergence to divergence. An explicit value of the threshold is derived for classes of attractive and repulsive graphs. The results show that a single repulsive link can sometimes drastically change the behavior of the consensus algorithm. They also explicitly show how the robustness of the consensus algorithm depends on the size and other properties of the graphs.

  • 27.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Proutière, Alexandre
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Continuous-time distributed optimization of homogenous dynamics2013Ingår i: 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013, IEEE conference proceedings, 2013, s. 520-527Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper makes an attempt to explore the fundamental properties of distributed methods for minimizing a sum of objective functions with each component only known to a particular node, given a certain level of node knowledge and computation capacity. The information each node receives from its neighbors can be any nonlinear function of its neighbors' states as long as the function takes value zero within the local consensus manifold. Each node also observes the gradient of its own objective function at its current state. The update dynamics of each node is a first-order integrator. The admissible control input of each node is homogeneous, given by a binary function with each variable corresponding to the neighboring term and the gradient term, respectively. The function determining the control law is assumed to be injective when the first variable is fixed to zero. It is proven that there exists a control rule which guarantees global optimal consensus if and only if the solution sets of the local objectives admit a nonempty intersection set for fixed strongly connected graphs. Then we show that for any tolerated error, we can find a simple control rule that guarantees global optimal consensus within this error for fixed, bidirectional, and connected graphs under mild conditions. For time-varying graphs, we show that optimal consensus can always be achieved by a simple control rule as long as the graph is uniformly jointly strongly connected and the nonempty intersection condition holds. The results illustrate that nonempty intersection for the local optimal solution sets is a critical condition for distributed optimization using consensus processing to connect the information over the nodes.

  • 28.
    Shi, Guodong
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Sou, Kin Cheong
    Chalmers University of Technology.
    Sandberg, Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    A graph-theoretic approach on optimizing informed-node selection in multi-agent tracking control2014Ingår i: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 267, s. 104-111Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A graph optimization problem for a multi-agent leader follower problem is considered. In a multi-agent system with n followers and one leader, each agent's goal is to track the leader using the information obtained from its neighbors. The neighborhood relationship is defined by a directed communication graph where k agents, designated as informed agents, can become neighbors of the leader. This paper establishes that, for any given strongly connected communication graph with k informed agents, all agents will converge to the leader. In addition, an upper bound and a lower bound of the convergence rate are obtained. These bounds are shown to explicitly depend on the maximal distance from the leader to the followers. The dependence between this distance and the exact convergence rate is verified by empirical studies. Then we show that minimizing the maximal distance problem is a metric k-center problem in classical combinatorial optimization studies, which can be approximately solved. Numerical examples are given to illustrate the properties of the approximate solutions.

  • 29.
    Terelius, Håkan
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Dowling, Jim
    Swedish Institute of Computer Science.
    Payberah, Amir
    Swedish Institute of Computer Science.
    Gattami, Ather
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Converging an Overlay Network to a Gradient Topology2011Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we investigate the topology convergence problem for the gossip-based Gradient overlay network. In an overlay network where each node has a local utility value, a Gradient overlay network is characterized by the properties that each node has a set of neighbors containing higher utility values, such that paths of increasing utilities emerge in the network topology. The Gradient overlay network is built using gossiping and a preference function that samples from nodes using a uniform random peer sampling service. We analyze it using tools from matrix analysis, and we prove both the necessary and sufficient conditions for convergence to a complete gradient structure, as well as estimating the convergence time. Finally, we show in simulations the potential of the Gradient overlay, by building a more efficient live-streaming peer-to-peer (P2P) system than one built using uniform random peer sampling.

  • 30.
    Terelius, Håkan
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Consensus Control for Multi-agent Systems with a Faulty Node2013Ingår i: 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems, IFAC Papers Online, 2013, s. 425-432Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper studies consensus control for a multi-agent system with a faulty node. The node dynamics follow a continuous-time consensus protocol with negative feedback from the relative state of the neighbors, where the faulty node is instead using positive feedback from the state. Conditions for reaching consensus are established, and a fault threshold is introduced. Numerical examples investigate how the fault threshold determines the system behavior. 

  • 31.
    Wu, Junfeng
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Probabilistic Convergence of Kalman Filtering over Nonstationary Fading Channels2014Ingår i: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, , s. 6s. 3783-3788Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with nonstationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(Pk), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of supk≥n Tr(Pk) and infk≥n Tr(Pk) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of infk≥n Tr(Pk) is provided.

  • 32.
    Wu, Junfeng
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Shi, Guodong
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Probabilistic Convergence of Kalman Filtering with Nonstationary Intermittent Observations2014Ingår i: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2014, s. 3783-3788Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we consider state estimation using a Kalman filter of a linear time-invariant process with non-stationary intermittent observations caused by packet losses. The packet loss process is modeled as a sequence of independent, but not necessarily identical Bernoulli random variables. Under this model, we show how the probabilistic convergence of the trace of the prediction error covariance matrices, which is denoted as Tr(P-k), depends on the statistical property of the nonstationary packet loss process. A series of sufficient and/or necessary conditions for the convergence of sup(k >= n) Tr(P-k) and inf(k >= n) Tr(P-k) are derived. In particular, for one-step observable linear system, a sufficient and necessary condition for the convergence of inf(k >= n) Tr(P-k) is provided.

  • 33. Yang, Tao
    et al.
    Meng, Ziyang
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Shi, Guodong
    Hong, Yiguang
    Johansson, Karl Henrik
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Synchronization for multi-agent systems under directed switching topologies2015Ingår i: Proceedings of the World Congress on Intelligent Control and Automation (WCICA), IEEE conference proceedings, 2015, nr March, s. 3473-3480Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we consider the synchronization problem for a network of state diffusive coupled agents with identical but time-varying dynamics under switching communication topologies. Both leader-follower and leaderless networks are studied. For leader-follower networks, sufficient conditions are established regarding the connectivity of communication graphs for the network to achieve global exponential or asymptotic synchronization, respectively, for directed and undirected communications. For leaderless networks, sufficient conditions for asymptotic norm synchronization are established, respectively, for directed and undirected communications, in the sense that the norm of agents' states converges to a common value. We also show that if the communication graph is fixed, norm synchronization leads to state synchronization. The results reveal some important similarities and differences between leaderless and leader-follower networks for synchronization under directed switching communication graphs.

1 - 33 av 33
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