Results 1  10
of
173
Continuum limit of selfdriven particles with orientation interaction
, 2007
"... We consider ..."
(Show Context)
From particle to kinetic and hydrodynamic descriptions of flocking
 Kinetic and Related Methods
"... Abstract. We discuss the CuckerSmale’s (CS) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasovtype kinetic model for the CS particle model and prove it exhibits timeasymptotic floc ..."
Abstract

Cited by 65 (5 self)
 Add to MetaCart
(Show Context)
Abstract. We discuss the CuckerSmale’s (CS) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasovtype kinetic model for the CS particle model and prove it exhibits timeasymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynamic description of flocking based on the CS Vlasovtype kinetic model and prove flocking behavior without closure of higher moments. 1. Introduction. Collective
Asymptotic Flocking Dynamics for the kinetic CuckerSmale model
, 2009
"... Abstract. In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting ..."
Abstract

Cited by 61 (14 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmanntype equation. The largetime behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.
On Krause’s MultiAgent Consensus Model With StateDependent Connectivity
"... Abstract—We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than one. We give a new proof of convergence into clusters of agents, with all agents i ..."
Abstract

Cited by 57 (8 self)
 Add to MetaCart
Abstract—We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than one. We give a new proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the intercluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on intercluster distances, under some mild assumptions. Index Terms—Consensus, decentralized control, multiagent system, opinion dynamics.
DOUBLE MILLING IN SELFPROPELLED SWARMS FROM KINETIC THEORY
"... (Communicated by Tong Yang) Abstract. We present a kinetic theory for swarming systems of interacting, selfpropelled discrete particles. Starting from the Liouville equation for the manybody problem we derive a kinetic equation for the single particle probability distribution function and the rela ..."
Abstract

Cited by 47 (13 self)
 Add to MetaCart
(Show Context)
(Communicated by Tong Yang) Abstract. We present a kinetic theory for swarming systems of interacting, selfpropelled discrete particles. Starting from the Liouville equation for the manybody problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other nontrivial morphologies such as compactly supported rotating mills. The kinetic theory approach leads us to the identification of macroscopic structures otherwise not recognized as solutions of the hydrodynamic equations, such as double mills of two superimposed flows. We find the conditions allowing for the existence of such solutions and compare to the case of single mills.
Decentralized, Adaptive Coverage Control for Networked Robots
, 2007
"... A decentralized, adaptive control law is presented to drive a network of mobile robots to an optimal sensing configuration. The control law is adaptive in that it uses sensor measurements to learn an approximation of the distribution of sensory information in the environment. It is decentralized in ..."
Abstract

Cited by 44 (7 self)
 Add to MetaCart
A decentralized, adaptive control law is presented to drive a network of mobile robots to an optimal sensing configuration. The control law is adaptive in that it uses sensor measurements to learn an approximation of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. The controller is then improved upon by implementing a consensus algorithm in parallel with the learning algorithm, greatly increasing parameter convergence rates. Convergence and consensus of parameters is proven. Finally, several variations on the learning algorithm are explored with a discussion of their stability in closed loop. The controller with and without parameter consensus is demonstrated in numerical simulations. These techniques are suggestive of broader applications of adaptive control methodologies to decentralized control problems in unknown dynamical environments. 1
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
Abstract

Cited by 41 (1 self)
 Add to MetaCart
(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
A simple proof of the CuckerSmale flocking dynamics and meanfield limit
 Comm. Math. Sci
"... Abstract. We present a simple proof on the formation of flocking to the CuckerSmale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large par ..."
Abstract

Cited by 40 (3 self)
 Add to MetaCart
Abstract. We present a simple proof on the formation of flocking to the CuckerSmale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large particle systems, we give a rigorous justification for the meanfield limit from the many particle CuckerSmale system to the Vlasov equation with flocking dissipation as the number of particles goes to infinity. Key words. Flocking, swarming, emergence, selfdriven particles system, autonomous agents, Vlasov equation, Lyapunov functional, measure valued solution, KantorovichRubinstein distance. Subject classifications. Primary 92C17; secondary 82C22, 82C40.
An overview of recent progress in the study of distributed multiagent coordination
, 2012
"... ..."
Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
Abstract

Cited by 33 (6 self)
 Add to MetaCart
(Show Context)
We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1