3,013 research outputs found
Enabling controlling complex networks with local topological information
Complex networks characterize the nature of internal/external interactions in real-world systems
including social, economic, biological, ecological, and technological networks. Two issues keep as
obstacles to fulflling control of large-scale networks: structural controllability which describes the
ability to guide a dynamical system from any initial state to any desired fnal state in fnite time, with a
suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost
for driving the network to a predefned state with a given number of control inputs. For large complex
networks without global information of network topology, both problems remain essentially open.
Here we combine graph theory and control theory for tackling the two problems in one go, using only
local network topology information. For the structural controllability problem, a distributed local-game
matching method is proposed, where every node plays a simple Bayesian game with local information
and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity.
Starring from any structural controllability solution, a minimizing longest control path method can
efciently reach a good solution for the optimal control in large networks. Our results provide solutions
for distributed complex network control and demonstrate a way to link the structural controllability and
optimal control together.The work was partially supported by National Science Foundation of China (61603209), and Beijing Natural Science Foundation (4164086), and the Study of Brain-Inspired Computing System of Tsinghua University program (20151080467), and Ministry of Education, Singapore, under contracts RG28/14, MOE2014-T2-1-028 and MOE2016-T2-1-119. Part of this work is an outcome of the Future Resilient Systems project at the Singapore-ETH Centre (SEC), which is funded by the National Research Foundation of Singapore (NRF) under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. (61603209 - National Science Foundation of China; 4164086 - Beijing Natural Science Foundation; 20151080467 - Study of Brain-Inspired Computing System of Tsinghua University program; RG28/14 - Ministry of Education, Singapore; MOE2014-T2-1-028 - Ministry of Education, Singapore; MOE2016-T2-1-119 - Ministry of Education, Singapore; National Research Foundation of Singapore (NRF) under Campus for Research Excellence and Technological Enterprise (CREATE) programme)Published versio
Resilience and Controllability of Dynamic Collective Behaviors
The network paradigm is used to gain insight into the structural root causes
of the resilience of consensus in dynamic collective behaviors, and to analyze
the controllability of the swarm dynamics. Here we devise the dynamic signaling
network which is the information transfer channel underpinning the swarm
dynamics of the directed interagent connectivity based on a topological
neighborhood of interactions. The study of the connectedness of the swarm
signaling network reveals the profound relationship between group size and
number of interacting neighbors, which is found to be in good agreement with
field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl.
Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic
collective behaviors enabling us to uncover that the swarm signaling network is
a homogeneous clustered small-world network, thus facilitating emergent
outcomes if connectedness is maintained. Resilience of the emergent consensus
is tested by introducing exogenous environmental noise, which ultimately
stresses how deeply intertwined are the swarm dynamics in the physical and
network spaces. The availability of the signaling network allows us to
analytically establish for the first time the number of driver agents necessary
to fully control the swarm dynamics
The Observability Radius of Networks
This paper studies the observability radius of network systems, which
measures the robustness of a network to perturbations of the edges. We consider
linear networks, where the dynamics are described by a weighted adjacency
matrix, and dedicated sensors are positioned at a subset of nodes. We allow for
perturbations of certain edge weights, with the objective of preventing
observability of some modes of the network dynamics. To comply with the network
setting, our work considers perturbations with a desired sparsity structure,
thus extending the classic literature on the observability radius of linear
systems. The paper proposes two sets of results. First, we propose an
optimization framework to determine a perturbation with smallest Frobenius norm
that renders a desired mode unobservable from the existing sensor nodes.
Second, we study the expected observability radius of networks with given
structure and random edge weights. We provide fundamental robustness bounds
dependent on the connectivity properties of the network and we analytically
characterize optimal perturbations of line and star networks, showing that line
networks are inherently more robust than star networks.Comment: 8 pages, 3 figure
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