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## SYNCHRONIZATION VIA PINNING CONTROL ON GENERAL COMPLEX NETWORKS (2013)

Citations: | 9 - 0 self |

### Citations

7695 |
Topics in Matrix Analysis
- Horn, Johnson
- 1999
(Show Context)
Citation Context ...trix G =(Gij)N×N . A directed edge Eij in network G is denoted by the ordered pair of vertices (vi,vj), where vi and vj are called the terminal and initial vertices, respectively. Definition 2.1 (see =-=[14]-=-). AnetworkGis undirected if there is a connection between vertices i and j in G; then Gij = Gji > 0; otherwise, Gij = Gji = 0 (i = j, i, j =1, 2,...,N). A network G is directed if there is a connect... |

3919 | Emergence of scaling in random networks
- Barabási, Albert
- 1999
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Citation Context ...ng tree, weakly connected network, directed forest AMS subject classifications. 93C10, 68M12, 93B25, 93A15 DOI. 10.1137/100781699 1. Introduction. Collective behaviors in complex networks and systems =-=[3, 10, 11, 28, 35, 39]-=- have attracted increasing attention in recent years due to their wide applications in physics, mathematics, engineering, biology, etc. Synchronization, similarly consensus, is a typical collective be... |

3316 |
Collective dynamics of “small-world” networks
- Watts, Strogatz
- 1998
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Citation Context ...ng tree, weakly connected network, directed forest AMS subject classifications. 93C10, 68M12, 93B25, 93A15 DOI. 10.1137/100781699 1. Introduction. Collective behaviors in complex networks and systems =-=[3, 10, 11, 28, 35, 39]-=- have attracted increasing attention in recent years due to their wide applications in physics, mathematics, engineering, biology, etc. Synchronization, similarly consensus, is a typical collective be... |

3047 | Choosability in graphs
- Erdős, Rubin, et al.
- 1979
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Citation Context ...ng tree, weakly connected network, directed forest AMS subject classifications. 93C10, 68M12, 93B25, 93A15 DOI. 10.1137/100781699 1. Introduction. Collective behaviors in complex networks and systems =-=[3, 10, 11, 28, 35, 39]-=- have attracted increasing attention in recent years due to their wide applications in physics, mathematics, engineering, biology, etc. Synchronization, similarly consensus, is a typical collective be... |

1107 | Consensus problems in networks of agents with switching topology and time-delays,” Automatic Control
- Olfati-Saber, Murray
- 2004
(Show Context)
Citation Context .../13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php a strongly connected directed network, G has one eigenvalue 0 with multiplicity 1 =-=[22]-=-. For an undirected or a balanced network, it is well known that 1N is not only the left eigenvector but also the right eigenvector of G associated with eigenvalue 0[29,30],thatis,G1N = 0N and 1T NG =... |

595 |
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556 |
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436 | Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
- Olfati-Saber
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Citation Context ...re, s(t) may be an equilibrium point, a periodic orbit, or even a chaotic solution, which can be viewed as the state of the reference vertex, or as the virtual leader in multi-agent dynamical systems =-=[23]-=-. The pinning strategy is applied on a small fraction δ (0 <δ<1) of vertices in the network [7, 54, 38]. Suppose that the vertices q1,q2,...,ql are selected to be pinned, where l = ⌊δN⌋ represents the... |

292 |
Handbook of Matrices,
- LUtkepohl
- 1996
(Show Context)
Citation Context ...T )/2+c G ⊗ (Γ + Γ T )/2 − c(ΞD) ⊗ (Γ + Γ T )/2 ≤ Ξ ⊗ (K + K T )/2Γ + c G ⊗ Γ − c(ΞD) ⊗ Γ ≤ (θΞ+c G − cΞD) ⊗ Γ. If θΞ +c( G − ΞD) < 0andΓ> 0, then it follows that condition (3.2) is satisfied =-=[20]-=-. Let C = θΞ+c( ( C11 − G − ΞD) = ˜ ) D C12 ˜C , where C11 and C12 are matrices with appropriate dimensions, ˜ D =diag(ξ1d1,...,ξldl), and ˜ C is obtained by removing the 1, 2,...,lrow-column pairs ... |

206 |
Combinatorial Matrix Theory
- Brualdi, Ryser
- 1991
(Show Context)
Citation Context ...ero matrix G of order 1 is irreducible. Next, a lemma is given to show the relation between an irreducible matrix and the corresponding strong connectivity in the network. Lemma 2.5 (Theorem 3.2.1 of =-=[5]-=-; Theorem 6.2.24 of [14]). AmatrixG is irreducible if and only if its corresponding network G is strongly connected. Lemma 2.5 is very easy to understand. For a strongly connected network, G can not b... |

137 | Stability of continuous-time distributed consensus algorithms, in: - Moreau - 2004 |

104 |
Zhou :The synchronization of chaotic systems.
- Boccaletti, Kurths, et al.
- 2002
(Show Context)
Citation Context ...ogy, etc. Synchronization, similarly consensus, is a typical collective behavior in complex dynamical networks and systems. Since the pioneering work of Pecora and Carroll [24], chaos synchronization =-=[2]-=- has received a great deal of attention due to its potential applications in secure communications, biological neural networks [47], genetic regulatory networks [57], parameter estimation, and so on. ... |

89 | C.: Synchronization in complex networks
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Citation Context ...ibited.1396 WENWU YU, GUANHONG CHEN, JINHU LÜ, AND JÜRGEN KURTHS Downloaded 04/05/13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php =-=[1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61]-=- and consensus [6, 51, 52, 53, 55, 59, 64] in very large-scale complex networks. First, local synchronization, meaning that synchronization can be reached within a certain region, was studied by the t... |

89 |
2002] “Synchronization in scale-free dynamical networks: Robustness and fragility
- Wang, Chen
(Show Context)
Citation Context ...ibited.1396 WENWU YU, GUANHONG CHEN, JINHU LÜ, AND JÜRGEN KURTHS Downloaded 04/05/13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php =-=[1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61]-=- and consensus [6, 51, 52, 53, 55, 59, 64] in very large-scale complex networks. First, local synchronization, meaning that synchronization can be reached within a certain region, was studied by the t... |

89 |
Synchronization in an array of linearly coupled dynamical systems”,
- Wu, Chua
- 1995
(Show Context)
Citation Context ...ation in time-varying complex networks was also reported [19]. For the global behavior, a distance function from the collective states of the network vertices to the synchronization manifold was used =-=[40, 44]-=- to study global synchronization of coupled networks and systems [18, 48, 49]. By designing some adaptive laws on the weights and coupling strength, synchronization in adaptive networks was shown [8, ... |

80 | A Time-Varying Complex Dynamical Network Model and Its Controlled Synchronization Criteria
- Lu, Chen
- 2005
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Citation Context ...ibited.1396 WENWU YU, GUANHONG CHEN, JINHU LÜ, AND JÜRGEN KURTHS Downloaded 04/05/13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php =-=[1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61]-=- and consensus [6, 51, 52, 53, 55, 59, 64] in very large-scale complex networks. First, local synchronization, meaning that synchronization can be reached within a certain region, was studied by the t... |

79 |
Large-scale Dynamic Systems. Stability and Structure,
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(Show Context)
Citation Context ... matrix G ∈ RN×N is nonnegative if every entry Gij ≥ 0(1≤i, j ≤ N), and a vector x ∈ RN is positive if every entry xi > 0(1≤i ≤ N). Matrix G in this paper is a singular and irreducible Metzler matrix =-=[31]-=-. In this paper, we focus on algebraic graph theory based on network topology and try to understand the basic principles for synchronization in directed complex networks. Lemma 2.7 (see [7]). If G is ... |

71 |
Distributed multi-vehicle coordinated control via local information exchange,”
- Ren, Atkins
- 2007
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Citation Context ...TN . However, for a general directed network, 1N is not the left eigenvector of G associated with eigenvalue 0. Since the left eigenvector is very important in determining the final asymptotic states =-=[27]-=-, the following property is derived. Lemma 2.11. Suppose that G is irreducible and satisfies ∑ N j=1 Gij =0with Gij ≥ 0(i= j). Then, there is a positive vector x such that GT x =0. Proof. Choose a po... |

56 |
Synchronization in small-world dynamical networks
- Wang, Chen
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48 |
On pinning synchronization of complex dynamical networks
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- 2009
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Citation Context ... all vertices in a large-scale network. To reduce the number of controlled vertices, some local feedback injections may be applied to a fraction of network vertices, which is known as pinning control =-=[7,9,12,15,16,17,25,26,32,33,34,38,42,43,45,46,54,62,63]-=-.Forexample,in the leader-follower control or distributed tracking problem, a group of mobile agents can coordinate so that they can track the leader [13, 50, 55]. The key issue is to design the appro... |

45 | Adaptive synchronization of an uncertain complex dynamical network
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41 |
Distributed observers design for leaderfollowing control of multi-agent networks.
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Citation Context ...2,15,16,17,25,26,32,33,34,38,42,43,45,46,54,62,63].Forexample,in the leader-follower control or distributed tracking problem, a group of mobile agents can coordinate so that they can track the leader =-=[13, 50, 55]-=-. The key issue is to design the appropriate control input where only a small fraction of agents can measure the leader’s information. The main objective in pinning control is to apply controllers on ... |

41 | Pinning control of scale-free dynamical networks
- Wang, Chen
- 2002
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Citation Context ...[18, 48, 49]. By designing some adaptive laws on the weights and coupling strength, synchronization in adaptive networks was shown [8, 60, 61]. In addition to the commonly studied undirected networks =-=[18, 19, 36, 37, 38, 45, 46, 48, 49, 61, 62]-=-, directed networks are also used to represent the interactive topology between the vertices. Actually, many real-world networks are directed, such as communication networks, the World Wide Web, email... |

40 |
Pinning a complex dynamical network to its equilibrium
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Citation Context ... all vertices in a large-scale network. To reduce the number of controlled vertices, some local feedback injections may be applied to a fraction of network vertices, which is known as pinning control =-=[7,9,12,15,16,17,25,26,32,33,34,38,42,43,45,46,54,62,63]-=-.Forexample,in the leader-follower control or distributed tracking problem, a group of mobile agents can coordinate so that they can track the leader [13, 50, 55]. The key issue is to design the appro... |

39 |
Synchronization in networks of nonlinear dynamical systems coupled via a directed graph”,
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Citation Context ..., email networks, and electrical power grids, to name just a few. Theoretically, the convergence analysis of synchronization for directed complex networks is more challenging than for undirected ones =-=[41]-=-. One contribution of this paper is that the convergence of a synchronization problem via pinning control on directed networks is theoretically analyzed, yielding some useful criteria for future appli... |

38 | Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,”
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Citation Context ...RTHS Downloaded 04/05/13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php [1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61] and consensus =-=[6, 51, 52, 53, 55, 59, 64]-=- in very large-scale complex networks. First, local synchronization, meaning that synchronization can be reached within a certain region, was studied by the transverse stability to the synchronization... |

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Citation Context ...ation in time-varying complex networks was also reported [19]. For the global behavior, a distance function from the collective states of the network vertices to the synchronization manifold was used =-=[40, 44]-=- to study global synchronization of coupled networks and systems [18, 48, 49]. By designing some adaptive laws on the weights and coupling strength, synchronization in adaptive networks was shown [8, ... |

34 | Pinning complex networks by a single controller
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Citation Context ... all vertices in a large-scale network. To reduce the number of controlled vertices, some local feedback injections may be applied to a fraction of network vertices, which is known as pinning control =-=[7,9,12,15,16,17,25,26,32,33,34,38,42,43,45,46,54,62,63]-=-.Forexample,in the leader-follower control or distributed tracking problem, a group of mobile agents can coordinate so that they can track the leader [13, 50, 55]. The key issue is to design the appro... |

33 | An overview of recent progress in the study of distributed multi-agent coordination,” - Cao, Yu, et al. - 2013 |

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Citation Context ...RTHS Downloaded 04/05/13 to 144.214.74.199. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php [1, 8, 18, 19, 36, 37, 48, 49, 56, 58, 60, 61] and consensus =-=[6, 51, 52, 53, 55, 59, 64]-=- in very large-scale complex networks. First, local synchronization, meaning that synchronization can be reached within a certain region, was studied by the transverse stability to the synchronization... |

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Citation Context ...[18, 48, 49]. By designing some adaptive laws on the weights and coupling strength, synchronization in adaptive networks was shown [8, 60, 61]. In addition to the commonly studied undirected networks =-=[18, 19, 36, 37, 38, 45, 46, 48, 49, 61, 62]-=-, directed networks are also used to represent the interactive topology between the vertices. Actually, many real-world networks are directed, such as communication networks, the World Wide Web, email... |

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Citation Context ...[18, 48, 49]. By designing some adaptive laws on the weights and coupling strength, synchronization in adaptive networks was shown [8, 60, 61]. In addition to the commonly studied undirected networks =-=[18, 19, 36, 37, 38, 45, 46, 48, 49, 61, 62]-=-, directed networks are also used to represent the interactive topology between the vertices. Actually, many real-world networks are directed, such as communication networks, the World Wide Web, email... |

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Citation Context ...Carroll [24], chaos synchronization [2] has received a great deal of attention due to its potential applications in secure communications, biological neural networks [47], genetic regulatory networks =-=[57]-=-, parameter estimation, and so on. In nature, there are large numbers of vertices in real-world complex networks, so it is of great interest to study network synchronization ∗Received by the editors J... |

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Citation Context ...the pioneering work of Pecora and Carroll [24], chaos synchronization [2] has received a great deal of attention due to its potential applications in secure communications, biological neural networks =-=[47]-=-, genetic regulatory networks [57], parameter estimation, and so on. In nature, there are large numbers of vertices in real-world complex networks, so it is of great interest to study network synchron... |

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1 |
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Citation Context ...genvalue 0 with multiplicity 1 [22]. For an undirected or a balanced network, it is well known that 1N is not only the left eigenvector but also the right eigenvector of G associated with eigenvalue 0=-=[29,30]-=-,thatis,G1N = 0N and 1T NG = 0TN . However, for a general directed network, 1N is not the left eigenvector of G associated with eigenvalue 0. Since the left eigenvector is very important in determinin... |

1 |
Switching control of a modified leader-follower team of agents under the leader and network topological changes
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Citation Context ...genvalue 0 with multiplicity 1 [22]. For an undirected or a balanced network, it is well known that 1N is not only the left eigenvector but also the right eigenvector of G associated with eigenvalue 0=-=[29,30]-=-,thatis,G1N = 0N and 1T NG = 0TN . However, for a general directed network, 1N is not the left eigenvector of G associated with eigenvalue 0. Since the left eigenvector is very important in determinin... |

1 |
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1 |
Pinning control of general multi-agent systems
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