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76
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An over ..."
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Cited by 279 (2 self)
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Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in smallworld networks, Markov processes and gossipbased algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with latticetype nearest neighbor interactions. Simulation results are presented that demonstrate the role of smallworld effects on the speed of consensus algorithms and cooperative control of multivehicle formations.
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 208 (5 self)
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Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of “gossip ” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the socalled Preferential Connectivity (PC) model.
2004a). Robust rendezvous for mobile autonomous agents via proximity graphs in d dimensions
 IEEE Transactions on Automatic Control. Submitted. Electronic
"... Abstract: This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arb ..."
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Cited by 111 (25 self)
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Abstract: This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arbitrary dimensions under weak requirements on the switching and failing communication topology. The correctness proof relies on proximity graphs and their properties and on a LaSalle Invariance Principle for nondeterministic discretetime systems. Copyright c ○ 2005 IFAC
Formations of vehicles in cyclic pursuit
 IEEE Transactions on Automatic Control
, 2004
"... Abstract—Inspired by the socalled “bugs ” problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system ..."
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Cited by 77 (1 self)
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Abstract—Inspired by the socalled “bugs ” problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the identical vehicles are ordered such that vehicle pursues vehicle CImodulo. In this paper, we assume each vehicle has the same constant forward speed. We show that the system’s equilibrium formations are generalized regular polygons and it is exposed how the multivehicle system’s global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not. Index Terms—Circulant matrices, cooperative control, multiagent systems, pursuit problems. I.
On partial contraction analysis for coupled nonlinear oscillators
 technical Report, Nonlinear Systems Laboratory, MIT
, 2003
"... We describe a simple but general method to analyze networks of coupled identical nonlinear oscillators, and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized)results on synchroni ..."
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Cited by 61 (33 self)
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We describe a simple but general method to analyze networks of coupled identical nonlinear oscillators, and study applications to fast synchronization, locomotion, and schooling. Specifically, we use nonlinear contraction theory to derive exact and global (rather than linearized)results on synchronization, antisynchronization and oscillatordeath. The method can be applied to coupled networks of various structures and arbitrary size. For oscillators with positivedefinite diffusion coupling, it can be shown that synchronization always occur globally for strong enough coupling strengths, and an explicit upper bound on the corresponding threshold can be computed through eigenvalue analysis. The discussion also extends to the case when network structure varies abruptly and asynchronously, as in “flocks ” of oscillators or dynamic elements.
Necessary and sufficient graphical conditions for formation control of unicycles,” technical report, http://www.control.utoronto.ca/people/profs/francis/publications.html
"... Abstract–The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the ..."
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Cited by 53 (0 self)
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Abstract–The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements. Index Terms–Multiagent system, distributed control, nonholonomic mobile robots. I.
Stability of continuoustime distributed consensus algorithms
, 2004
"... We study the stability properties of linear timevarying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibri ..."
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Cited by 51 (0 self)
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We study the stability properties of linear timevarying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the offdiagonal terms in the differential equation.
Stable concurrent synchronization in dynamic system networks
 Neural Networks
, 2007
"... In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple “rhythms ” interacting and functional assemblies combining neural oscillators of ..."
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Cited by 28 (17 self)
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In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple “rhythms ” interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flowinvariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed. 1
Multiagent Kalman consensus with relative uncertainty
 IN PROC. OF ACC
, 2005
"... In this paper, we propose discretetime and continuoustime consensus update schemes motivated by the discretetime and continuoustime Kalman filters. With certainty information encoded into each agent, the proposed consensus schemes explicitly account for relative confidence / reliability of inf ..."
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Cited by 22 (1 self)
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In this paper, we propose discretetime and continuoustime consensus update schemes motivated by the discretetime and continuoustime Kalman filters. With certainty information encoded into each agent, the proposed consensus schemes explicitly account for relative confidence / reliability of information states from each agent in the team. We show mild sufficient conditions under which consensus can be achieved using the proposed consensus schemes in the presence of switching interaction topologies.
Distributed geodesic control laws for flocking of nonholonomic agents
 IEEE Transaction on Automatic Control
, 2005
"... Abstract—We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3D motion), we develop a geodesic control law that minimizes a misalignment ..."
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Cited by 17 (4 self)
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Abstract—We study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions. By analyzing the velocity vectors of agents on a circle (for planar motion) or sphere (for 3D motion), we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking. The proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected. We further show that flocking is possible even when the topology of the proximity graph changes over time, so long as a weaker notion of joint connectivity is preserved. Index Terms—Cooperative control, distributed coordination, flocking, multiagent systems. I.