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28
Synchronization in Networks of Identical Linear Systems
, 2008
"... The paper investigates the synchronization of a network of identical linear statespace models under a possibly timevarying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have n ..."
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Cited by 46 (0 self)
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The paper investigates the synchronization of a network of identical linear statespace models under a possibly timevarying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient – but to some extent, also necessary – to ensure synchronization with the diffusive static output coupling often considered in the literature. 1
Stabilization of collective motion in three dimensions: A consensus approach
 Proc. 46th IEEE Conf. Decision and Control
, 2007
"... Abstract — This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in threedimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem. We ..."
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Cited by 21 (8 self)
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Abstract — This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in threedimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem. We first derive the stabilizing control laws in the presence of alltoall communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and timevarying communication topologies. I.
Synchronization of Interconnected Systems With Applications to Biochemical Networks: An InputOutput Approach
, 2010
"... This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as “compartments ” in this paper) are made up of an identical interconnection of subsystems, each represented as an operator in an extended 2 space and referred to as a “spec ..."
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Cited by 17 (4 self)
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This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as “compartments ” in this paper) are made up of an identical interconnection of subsystems, each represented as an operator in an extended 2 space and referred to as a “species.” The compartments are, in turn, coupled through a diffusionlike term among the respective species. The synchronization conditions are provided by combining the inputoutput properties of the subsystems with information about the structure of the network. The paper also explores results for statespace models, as well as biochemical applications. The work is motivated by cellular networks where signaling occurs both internally, through interactions of species, and externally, through intercellular signaling. The theory is illustrated by providing synchronization conditions for networks of Goodwin oscillators.
THE TOTAL sENERGY OF A MULTIAGENT SYSTEM
 SIAM J. CONTROL OPTIM, VOL. 49, NO. 4, PP. 1680–1706
, 2011
"... We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology ..."
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Cited by 16 (6 self)
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We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology.
Exploring Synchronization in Complex Oscillator Networks
"... Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of hetero ..."
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Cited by 11 (1 self)
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Abstract — The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among the oscillators. These two ingredients give rise to a rich dynamic behavior that keeps on fascinating the scientific community. In this article, we present a tutorial introduction to coupled oscillator networks, we review the vast literature on theory and applications, and we present a collection of different synchronization notions, conditions, and analysis approaches. We focus on the canonical phase oscillator models occurring in countless realworld synchronization phenomena, and present their rich phenomenology. We review a set of applications relevant to control scientists. We explore different approaches to phase and frequency synchronization, and we present a collection of synchronization conditions and performance estimates. For all results we present selfcontained proofs that illustrate a sample of different analysis methods in a tutorial style. I.
Distributed clock synchronization: Joint frequency and phase consensus.”
 In Proceeding of the 50th IEEE Conference on Decision and Control, and European Control Conference,
, 2011
"... AbstractDistributed synchronization has gradually gained importance over the last two decades. The adhoc nature of new applications has increased the need for robust and scalable distributed algorithms that are capable of generating high precision timing information. However, current solutions us ..."
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Cited by 11 (5 self)
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AbstractDistributed synchronization has gradually gained importance over the last two decades. The adhoc nature of new applications has increased the need for robust and scalable distributed algorithms that are capable of generating high precision timing information. However, current solutions usually produce phase errors when the frequencies are heterogeneous. This paper proposes a distributed synchronization procedure that can achieve consensus in both frequency and phase. The algorithm uses only local information and is robust to frequency heterogeneity and network topology. A sufficient condition for global convergence is shown by leveraging recent results on coupled oscillators. We further characterize an invariant constant of the algorithm that relates the limiting frequency ω * with the harmonic mean of the clocks' natural frequencies. Simulations are provided to illustrate and verify these properties.
Stabilization of ThreeDimensional Collective Motion
, 2008
"... This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in threedimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algeb ..."
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Cited by 10 (3 self)
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This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in threedimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We first derive the stabilizing control laws in the presence of alltoall communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and timevarying communication topologies.
Alternating spatial patterns for coordinated group motion
 Proc. 46th IEEE Conf. Decision and Control
, 2007
"... Abstract — Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns ..."
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Cited by 8 (6 self)
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Abstract — Motivated by recent observations of fish schools, we study coordinated group motion for individuals with oscillatory speed. Neighbors that have speed oscillations with common frequency, amplitude and average but different phases, move together in alternating spatial patterns, taking turns being towards the front, sides and back of the group. We propose a model and control laws to investigate the connections between these spatial dynamics, communication when sensing is range or direction limited, and convergence of coordinated group motions. I.
Cooperative attitude synchronization in satellite swarms: a consensus approach
 Proc. 17th IFAC Symp. Automatic Control in Aerospace
, 2007
"... Abstract: The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as particles on SO(3) and drive these particles to a common point in SO(3). Unlike the Euler angl ..."
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Cited by 5 (1 self)
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Abstract: The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as particles on SO(3) and drive these particles to a common point in SO(3). Unlike the Euler angle or quaternion descriptions, this model suffers no singularities nor doublepoints. Our approach is fully cooperative and autonomous: we use no leader nor external reference. We present two types of control laws, in terms of applied control torques, that globally drive the swarm towards attitude synchronization: one that requires treelike or alltoall intersatellite communication (most efficient) and one that works with nearly arbitrary communication (most robust).