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95
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 616 (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.
Information Consensus in Multivehicle Cooperative Control
, 2007
"... The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be rea ..."
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Cited by 199 (23 self)
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The abundance of embedded computational resources in autonomous vehicles enables enhanced operational effectiveness through cooperative teamwork in civilian and military applications. Compared to autonomous vehicles that perform solo missions, greater efficiency and operational capability can be realized from teams of autonomous vehicles operating in a coordinated fashion. Potential applications for multivehicle systems include spacebased interferometers, combat, surveillance, and reconnaissance systems, hazardous material handling, and distributed reconfigurable sensor networks. To enable these applications, various cooperative control capabilities need to be developed, including formation control, rendezvous, attitude alignment, flocking, foraging, task and role assign
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 125 (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.
Stabilization of planar collective motion with limited communication
 IEEE Trans. Automat. Contr
"... Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particle ..."
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Cited by 80 (29 self)
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Abstract—This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and timeinvariant or timevarying. The emphasis of this paper is to show how previous results assuming alltoall communication can be extended to a general communication framework. Index Terms—Cooperative control, geometric control, multiagent systems, stabilization. I.
Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators
 IEEE Transactions on Automatic Control
, 2010
"... Abstract — Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the networkreduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model ..."
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Cited by 67 (14 self)
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Abstract — Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the networkreduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a firstorder model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform Kuramoto model characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. By extending methods from synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to and improve upon previouslyavailable tests for the classic Kuramoto model. By combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying network parameters and initial conditions. I.
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 45 (23 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
State agreement for continuoustime coupled nonlinear systems
 SIAM Journal on Control and Optimization
, 2007
"... Abstract. Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interactio ..."
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Cited by 42 (2 self)
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Abstract. Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. Generalizing the work of Moreau, under the assumption that the vector fields satisfy a certain subtangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. The proof uses nonsmooth analysis. Secondly, the rendezvous problem for kinematic pointmass mobile robots is studied when the robots ’ fields of view have a fixed radius. The circumcenter control law of Ando et al. [1] is shown to solve the problem. The rendezvous problem is a kind of state agreement problem, but the interaction structure is state dependent.
Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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Cited by 31 (0 self)
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1
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 30 (6 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.
Passivitybased control of multiagent systems
 ADVANCES IN ROBOT CONTROL: FROM EVERYDAY PHYSICS TO HUMANLIKE MOVEMENTS
"... In this paper we study passivitybased control for the problem of coordination and synchronization of multiagent systems. We treat agents described by affine nonlinear systems that are inputoutput passive and that exchange information over a network described by an interconnection graph. We tre ..."
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Cited by 29 (2 self)
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In this paper we study passivitybased control for the problem of coordination and synchronization of multiagent systems. We treat agents described by affine nonlinear systems that are inputoutput passive and that exchange information over a network described by an interconnection graph. We treat both linear interconnections on balanced, directed graphs and nonlinear interconnections on undirected graphs. We present synchronization results for both fixed and switching graphs. Finally, we treat the realistic case of time delay in the communication of information among agents. Our results unify several existing results from the literature on multiagent systems. As applications of our results we present a constructive methodology to solve the local exponential convergence problem for Kuramoto oscillators. We then apply our results to the general problem of synchronization of multiple Lagrangian systems. Using a network of simple pendula, the phenomena of oscillator death, synchronization, and antisynchronization are all shown to be special cases of our results, depending on whether or not the natural frequencies of the pendula are identical or distinct. We also show that the general problem of multirobot coordination can be handled using the results in this paper.