6,080 research outputs found
The Most Exigent Eigenvalue: Guaranteeing Consensus under an Unknown Communication Topology and Time Delays
This document aims to answer the question of what is the minimum delay value
that guarantees convergence to consensus for a group of second order agents
operating under different protocols, provided that the communication topology
is connected but unknown. That is, for all the possible communication
topologies, which value of the delay guarantees stability? To answer this
question we revisit the concept of most exigent eigenvalue, applying it to two
different consensus protocols for agents driven by second order dynamics. We
show how the delay margin depends on the structure of the consensus protocol
and the communication topology, and arrive to a boundary that guarantees
consensus for any connected communication topology. The switching topologies
case is also studied. It is shown that for one protocol the stability of the
individual topologies is sufficient to guarantee consensus in the switching
case, whereas for the other one it is not
Consensus in multi-agent systems with non-periodic sampled-data exchange and uncertain network topology
In this paper consensus in second-order multi-agent systems with a
non-periodic sampled-data exchange among agents is investigated. The sampling
is random with bounded inter-sampling intervals. It is assumed that each agent
has exact knowledge of its own state at any time instant. The considered local
interaction rule is PD-type. Sufficient conditions for stability of the
consensus protocol to a time-invariant value are derived based on LMIs. Such
conditions only require the knowledge of the connectivity of the graph modeling
the network topology. Numerical simulations are presented to corroborate the
theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1407.300
Consensus problems in networks of agents with switching topology and time-delays
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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