Consensus problems in networks of agents with switching topology and time-delays
TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
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Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
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References
Flocks, herds and schools: A distributed behavioral model
Craig W. Reynolds
- 01 Aug 1987
TL;DR: In this article, an approach based on simulation as an alternative to scripting the paths of each bird individually is explored, with the simulated birds being the particles and the aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course.
•Book
Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
- 01 Jan 2009
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Exploring complex networks
TL;DR: This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture.
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TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Novel Type of Phase Transition in a System of Self-Driven Particles
TL;DR: Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.
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