TY - JOUR
T1 - Leader-follower consensus over numerosity-constrained random networks
AU - Abaid, Nicole
AU - Porfiri, Maurizio
N1 - Funding Information:
Maurizio Porfiri was born in Rome, Italy in 1976. He received his M.Sc. and Ph.D. degrees in Engineering Mechanics from Virginia Tech, in 2000 and 2006; a “Laurea” in Electrical Engineering (with honors) and a Ph.D. in Theoretical and Applied Mechanics from the University of Rome “La Sapienza” and the University of Toulon (dual degree program), in 2001 and 2005, respectively. From 2005 to 2006 he held a Post-doctoral position with the Electrical and Computer Engineering Department at Virginia Tech. He has been a member of the Faculty of the Mechanical and Aerospace Engineering Department of the Polytechnic Institute of New York University since 2006, where he is currently an Associate Professor. He is engaged in conducting and supervising research on dynamical systems theory, multiphysics modeling, and underwater robotics. Maurizio Porfiri is the recipient of the NSF CAREER award (Dynamical Systems program) in 2008, he has been included in the “Brilliant 10” list of Popular Science in 2010, and he has received the Outstanding Young Alumnus award by the College of Engineering of Virginia Tech in 2012.
Funding Information:
This work was supported by the National Science Foundation under Grant # CMMI-0745753 and GK-12 Fellows Grant # DGE-0741714 . The material in this paper was partially presented at the 2011 ASME DSCC Dynamic Systems and Control Conference, October 31–November 2, 2011, Arlington, Virginia, USA. This paper was recommended for publication in revised form by Associate Editor Valery Ugrinovskii under the direction of Editor Ian R. Petersen.
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/8
Y1 - 2012/8
N2 - In this work, we study a discrete-time consensus protocol for a group of agents which communicate over a class of stochastically switching networks inspired by fish schooling. The network model incorporates the phenomenon of numerosity, that plays a prominent role in the collective behavior of animal groups, by defining the individuals' perception of numbers. The agents comprise leaders, which share a common state, and followers, which update their states based on information exchange among neighboring agents. We establish a closed form expression for the asymptotic convergence factor of the protocol, that measures the decay rate of disagreement among the followers' and the leaders' states. Handleable forms of this expression are derived for the physically relevant cases of large networks whose agents are composed of primarily leaders or followers. Numerical simulations are conducted to validate analytical results and illustrate the consensus dynamics as a function of the number of leaders in the group, the agents' persuasibility, and the agents' numerosity. We find that the maximum speed of convergence for a given population can be enhanced by increasing the proportion of leaders in the group or the agents' numerosity. On the other hand, we find that increasing the numerosity has also a negative effect as it reduces the range of agents' persuasibility for which consensus is possible. Finally, we compare the main features of this leader-follower consensus protocol with its leaderless counterpart to elucidate the benefits and drawbacks of leadership in numerosity-constrained random networks.
AB - In this work, we study a discrete-time consensus protocol for a group of agents which communicate over a class of stochastically switching networks inspired by fish schooling. The network model incorporates the phenomenon of numerosity, that plays a prominent role in the collective behavior of animal groups, by defining the individuals' perception of numbers. The agents comprise leaders, which share a common state, and followers, which update their states based on information exchange among neighboring agents. We establish a closed form expression for the asymptotic convergence factor of the protocol, that measures the decay rate of disagreement among the followers' and the leaders' states. Handleable forms of this expression are derived for the physically relevant cases of large networks whose agents are composed of primarily leaders or followers. Numerical simulations are conducted to validate analytical results and illustrate the consensus dynamics as a function of the number of leaders in the group, the agents' persuasibility, and the agents' numerosity. We find that the maximum speed of convergence for a given population can be enhanced by increasing the proportion of leaders in the group or the agents' numerosity. On the other hand, we find that increasing the numerosity has also a negative effect as it reduces the range of agents' persuasibility for which consensus is possible. Finally, we compare the main features of this leader-follower consensus protocol with its leaderless counterpart to elucidate the benefits and drawbacks of leadership in numerosity-constrained random networks.
KW - Consensus
KW - Convergence factor
KW - Multi-agent coordination
KW - Random networks
KW - Stochastic stability
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U2 - 10.1016/j.automatica.2012.05.058
DO - 10.1016/j.automatica.2012.05.058
M3 - Article
AN - SCOPUS:84864449077
SN - 0005-1098
VL - 48
SP - 1845
EP - 1851
JO - Automatica
JF - Automatica
IS - 8
ER -