14,505 research outputs found
Decomposing the dynamics of heterogeneous delayed networks with applications to connected vehicle systems
Delay-coupled networks are investigated with nonidentical delay times and the
effects of such heterogeneity on the emergent dynamics of complex systems are
characterized. A simple decomposition method is presented that decouples the
dynamics of the network into node-size modal equations in the vicinity of
equilibria. The resulting independent components contain distributed delays
that map the spatiotemporal complexity of the system to the time domain. We
demonstrate that this new approach can be used to reveal new physical phenomena
in heterogenous vehicular traffic when vehicles are linked via
vehicle-to-vehicle (V2V) communication.Comment: The paper has been updated in response to referee comments. 5 pages,
2 figure
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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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