17,124 research outputs found
Local pinning of networks of multi-agent systems with transmission and pinning delays
We study the stability of networks of multi-agent systems with local pinning
strategies and two types of time delays, namely the transmission delay in the
network and the pinning delay of the controllers. Sufficient conditions for
stability are derived under specific scenarios by computing or estimating the
dominant eigenvalue of the characteristic equation. In addition, controlling
the network by pinning a single node is studied. Moreover, perturbation methods
are employed to derive conditions in the limit of small and large pinning
strengths.Numerical algorithms are proposed to verify stability, and simulation
examples are presented to confirm the efficiency of analytic results.Comment: 6 pages, 3 figure
Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks
Recent advances in electronics are enabling substantial processing to be
performed at each node (robots, sensors) of a networked system. Local
processing enables data compression and may mitigate measurement noise, but it
is still slower compared to a central computer (it entails a larger
computational delay). However, while nodes can process the data in parallel,
the centralized computational is sequential in nature. On the other hand, if a
node sends raw data to a central computer for processing, it incurs
communication delay. This leads to a fundamental communication-computation
trade-off, where each node has to decide on the optimal amount of preprocessing
in order to maximize the network performance. We consider a network in charge
of estimating the state of a dynamical system and provide three contributions.
First, we provide a rigorous problem formulation for optimal real-time
estimation in processing networks in the presence of delays. Second, we show
that, in the case of a homogeneous network (where all sensors have the same
computation) that monitors a continuous-time scalar linear system, the optimal
amount of local preprocessing maximizing the network estimation performance can
be computed analytically. Third, we consider the realistic case of a
heterogeneous network monitoring a discrete-time multi-variate linear system
and provide algorithms to decide on suitable preprocessing at each node, and to
select a sensor subset when computational constraints make using all sensors
suboptimal. Numerical simulations show that selecting the sensors is crucial.
Moreover, we show that if the nodes apply the preprocessing policy suggested by
our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio
Complex transitions to synchronization in delay-coupled networks of logistic maps
A network of delay-coupled logistic maps exhibits two different
synchronization regimes, depending on the distribution of the coupling delay
times. When the delays are homogeneous throughout the network, the network
synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92,
144101 (2004)], which may be periodic or chaotic depending on the delay; when
the delays are sufficiently heterogeneous, the synchronization proceeds to a
steady-state, which is unstable for the uncoupled map [Masoller and Marti,
Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from
time-dependent to steady-state synchronization as the width of the delay
distribution increases. We also compare the two transitions to synchronization
as the coupling strength increases. We use transition probabilities calculated
via symbolic analysis and ordinal patterns. We find that, as the coupling
strength increases, before the onset of steady-state synchronization the
network splits into two clusters which are in anti-phase relation with each
other. On the other hand, with increasing delay heterogeneity, no cluster
formation is seen at the onset of steady-state synchronization; however, a
rather complex unsynchronized state is detected, revealed by a diversity of
transition probabilities in the network nodes
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