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## Consensus Problems in Networks of Agents with Switching Topology and Time-Delays (2003)

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Citations: | 1112 - 21 self |

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Citation Context ...satellites, and congestion control in communication networks [10]. Consensus problems have a long history in the field of computer science, particularly in automata theory and distributed computation =-=[11]-=-. In many applications involving multiagent/multivehicle systems, groups of agents need to agree upon certain quantities of interest. Such quantities might or might not be related to the motion of the... |

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Citation Context ...EBRAIC GRAPH THEORY AND MATRIX THEORY In this section, we introduce some basic concepts and notation in graph theory that will be used throughout this paper. More information is available in [31] and =-=[37]-=-. A comprehensive survey on properties of Laplacians of undirected graphs can be found in [38]. However, we need to use some basic properties of Laplacians of digraphs. These properties cannot be foun... |

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Citation Context ...eory. Here, our main focus is analysis of consensus protocols on directed networks with fixed/switching topology. In this paper, our analysis relies on several tools from algebraic graph theory [30], =-=[31]-=-, matrix theory [32], and control theory. We establish a connection between the performance of a linear consensus protocol on a directed network and the Fiedler eigenvalue of the mirror graph of the i... |

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Citation Context ...ing well-known property holds [31]: (17) The proof follows from a special case of Courant–Fischer Theorem in [32]. We will later establish a connection between with , called the Fiedler eigenvalue of =-=[39]-=- and the performance (i.e., worst case speed of convergence) of protocol (A1) on digraphs. Remark 5: The notion of algebraic connectivity (or ) of graphs was originally defined by Fiedler for undirect... |

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Citation Context ...ation of all agents. In recent years, there has been a tremendous amount of renewed interest in flocking/swarming [20]–[27] that has been primarily originated from the pioneering work of Reynolds. In =-=[7]-=-, alignment of heading angles for multiple particles is analyzed from the point of view of statistical mechanics. Moreover, a phase transition phenomenon is observed that occurs when the network topol... |

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Citation Context ...rchers in recent years. This is partly due to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control [1]–[5], flocking =-=[6]-=-–[8], distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks [10]. Consensus problems have a long history in the field of compu... |

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Citation Context ...cted several researchers in recent years. This is partly due to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control =-=[1]-=-–[5], flocking [6]–[8], distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks [10]. Consensus problems have a long history in ... |

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Citation Context ...weights in protocol (A1) such that a certain performance index is maximized (or minimized) is an optimization problem that falls within the category of network design problems. We refer the reader to =-=[34]-=- for a network design problem for reaching average-consensus using a semidefinite programming approach. The framework presented in [34] partially relies on the work in [29] that introduced average-con... |

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Citation Context ...ation of coupled oscillators, a consensus is reached regarding the frequency of oscillation of all agents. In recent years, there has been a tremendous amount of renewed interest in flocking/swarming =-=[20]-=-–[27] that has been primarily originated from the pioneering work of Reynolds. In [7], alignment of heading angles for multiple particles is analyzed from the point of view of statistical mechanics. M... |

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Citation Context ... systems with nonlinear dynamics that are not feedback linearizable. A special case of this approach is known as the leader–follower architecture and has been widely used by numerous researchers [13]–=-=[15]-=-. In [16], graph Laplacians are used as an essential part of a dynamic theory of graphs. The problem of synchronization of coupled oscillators is closely related to consensus problems on graphs. This ... |

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Citation Context ...anned air vehicles (UAVs), formation control [1]–[5], flocking [6]–[8], distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks =-=[10]-=-. Consensus problems have a long history in the field of computer science, particularly in automata theory and distributed computation [11]. In many applications involving multiagent/multivehicle syst... |

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Citation Context ...s. This is different than the approach pursued in the work of Jadbabaie et al. which strongly relies on matrix theoretic properties and infinite right-convergent products (RCP) of stochastic matrices =-=[36]-=-. V. ALGEBRAIC GRAPH THEORY AND MATRIX THEORY In this section, we introduce some basic concepts and notation in graph theory that will be used throughout this paper. More information is available in [... |

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Citation Context ...ich the agents have simple dynamics motivated by the model used in [7]. It is shown that the connectivity of the graph on average is sufficient for convergence of the heading angles of the agents. In =-=[29]-=-, the authors provide a convergence analysis of linear and nonlinear 0018-9286/04$20.00 © 2004 IEEE OLFATI-SABER AND MURRAY: CONSENSUS PROBLEMS IN NETWORKS OF AGENTS 1521 protocols for undirected netw... |

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Citation Context ...stochastic matrix for all . We refer to as the Perron matrix induced by . The convergence analysis of protocol (A1) for discrete-time agents heavily relies on the theory of nonnegative matrices [32], =-=[35]-=- and will be discussed in a separate paper. Our approach presents a Lyapunov-based convergence analysis for agreement in networks with discrete-time models. This is different than the approach pursued... |

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Citation Context ...y due to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control [1]–[5], flocking [6]–[8], distributed sensor networks =-=[9]-=-, attitude alignment of clusters of satellites, and congestion control in communication networks [10]. Consensus problems have a long history in the field of computer science, particularly in automata... |

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Citation Context ...tation in graph theory that will be used throughout this paper. More information is available in [31] and [37]. A comprehensive survey on properties of Laplacians of undirected graphs can be found in =-=[38]-=-. However, we need to use some basic properties of Laplacians of digraphs. These properties cannot be found in the graph theory literature and will be stated here. Let be a weighted directed graph (or... |

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Citation Context ...statistical mechanics. Moreover, a phase transition phenomenon is observed that occurs when the network topology becomes connected by increasing the density of agents in a bounded region. The work in =-=[28]-=- focuses on attitude alignment on undirected graphs in which the agents have simple dynamics motivated by the model used in [7]. It is shown that the connectivity of the graph on average is sufficient... |

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Citation Context ... several researchers in recent years. This is partly due to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control [1]–=-=[5]-=-, flocking [6]–[8], distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks [10]. Consensus problems have a long history in the ... |

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Citation Context ...ed to systems with nonlinear dynamics that are not feedback linearizable. A special case of this approach is known as the leader–follower architecture and has been widely used by numerous researchers =-=[13]-=-–[15]. In [16], graph Laplacians are used as an essential part of a dynamic theory of graphs. The problem of synchronization of coupled oscillators is closely related to consensus problems on graphs. ... |

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Citation Context ...ems that are essentially different forms of agreement problems with differences regarding the types of agent dynamics, the properties of the graphs, and the names of the tasks of interest. In [1] and =-=[12]-=-, graph Laplacians are used for the task of formation stabilization for groups of agents with linear dynamics. This particular method for formation stabilization has not yet been extended to systems w... |

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Citation Context ...rs in recent years. This is partly due to broad applications of multiagent systems in many areas including cooperative control of unmanned air vehicles (UAVs), formation control [1]–[5], flocking [6]–=-=[8]-=-, distributed sensor networks [9], attitude alignment of clusters of satellites, and congestion control in communication networks [10]. Consensus problems have a long history in the field of computer ... |

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Citation Context ...f coupled oscillators is closely related to consensus problems on graphs. This is a broad field that is of great interest to researchers in physics, biophysics, neurobiology, and systems biology [17]–=-=[19]-=-. In synchronization of coupled oscillators, a consensus is reached regarding the frequency of oscillation of all agents. In recent years, there has been a tremendous amount of renewed interest in flo... |

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Citation Context ...with nonlinear dynamics that are not feedback linearizable. A special case of this approach is known as the leader–follower architecture and has been widely used by numerous researchers [13]–[15]. In =-=[16]-=-, graph Laplacians are used as an essential part of a dynamic theory of graphs. The problem of synchronization of coupled oscillators is closely related to consensus problems on graphs. This is a broa... |

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Citation Context ... of coupled oscillators, a consensus is reached regarding the frequency of oscillation of all agents. In recent years, there has been a tremendous amount of renewed interest in flocking/swarming [20]–=-=[27]-=- that has been primarily originated from the pioneering work of Reynolds. In [7], alignment of heading angles for multiple particles is analyzed from the point of view of statistical mechanics. Moreov... |

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Citation Context ... communication and interagent sensing costs limited. We define the communication/sensing cost of the topology ( , ) of a protocol as , or the total number of the directed edges of the graph ( , ). In =-=[33]-=-, is called “communication complexity” of performing a task. For weighted digraphs, the communication/sensing cost can be defined as a function of the adjacency elements by (7) where is the sign funct... |

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