1,842 research outputs found
Synchronization with partial state coupling on SO(n)
This paper studies autonomous synchronization of k agents whose states evolve
on SO(n), but which are only coupled through the action of their states on one
"reference vector" in Rn for each link. Thus each link conveys only partial
state information at each time, and to reach synchronization agents must
combine this information over time or throughout the network. A natural
gradient coupling law for synchronization is proposed. Extensive convergence
analysis of the coupled agents is provided, both for fixed and time-varying
reference vectors. The case of SO(3) with fixed reference vectors is discussed
in more detail. For comparison, we also treat the equivalent setting in Rn,
i.e. with states in Rn and connected agents comparing scalar product of their
states with a reference vector.Comment: to be submitted to SIAM Journal on Control and Optimizatio
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
A General Model of Opinion Dynamics with Tunable Sensitivity
We introduce a general model of continuous-time opinion dynamics for an
arbitrary number of agents that communicate over a network and form real-valued
opinions about an arbitrary number of options. Drawing inspiration from models
in biology, physics, and social psychology, we apply a sigmoidal saturating
function to inter-agent and intra-agent exchanges of opinions. The saturating
function is the only nonlinearity in the model, yet we prove how it yields
rapid and reliable formation of consensus, dissensus, and opinion cascades as a
function of just a few parameters. We further show how the network opinion
dynamics exhibit both robustness to disturbance and ultrasensitivity to inputs.
We design feedback dynamics for system parameters that enable active tuning of
implicit thresholds in opinion formation for sensitivity to inputs, robustness
to changes in input, opinion cascades, and flexible transitions between
consensus and dissensus. The general model can be used for systematic control
design in a range of engineering problems including network systems,
multi-robot coordination, task allocation, and decision making for spatial
navigation. It can also be used for systematic examination of questions in
biology and social science ranging from cognitive control and networks in the
brain, to resilience in collective animal behavior to changing environmental
conditions, to information spreading and political polarization in social
networks
Stability and String Stability Analysis of Formation Control Architectures for Platooning.
This thesis presents theoretical results for stability and string stability
of formation control architectures for platooning. We consider
three important interconnection topologies for vehicles travelling in a
straight line as a string: leader following, cyclic and bidirectional.
For the leader following topology we discuss modifications that allow
reduced coordination requirements. In the first case we consider
the use of the leader velocity as the state to be broadcast to the followers,
rather than the standard use of the leader position. This selection
yields a formation control architecture that achieves string stability
even under time delays in the state broadcast, while reducing typical
coordination requirements of leader following architectures. For the
second modification we change the way in which the leader position
is sent across the string to every follower. This technique keeps some
of the good transient properties of the standard leader following architecture
but eliminates most of the coordination requirements for
the followers. However, we show that this technique does not provide
string stability when time delays are present in the communication.
The second topology that we discuss is a cyclic one, where the first
member of the platoon is forced to track the last one. We discuss two
strategies: one where the inter-vehicle spacings may follow a constanttime
headway spacing policy and one where an independent leader
broadcasts its position to every member of a cyclic platoon. For both
strategies we obtain closed form expressions for the transfer functions
from disturbances to inter-vehicle spacings. These expressions allow
us to show that if the design parameters are not properly chosen, the
vehicle platoon may become unstable when the string size is greater
than a critical number. On the contrary, if the design parameters are
well chosen, both architectures can be made stable and string stable
for any size of the platoon.
The final topology that we consider is bidirectional, where every
member of the platoon, with the exception of the first and last, use
measurements of the two nearest neighbours to control their position
within the string. Although the derivations are more complex than
in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in
the form of simple transfer functions from disturbances to vehicles.
They allow us to obtain stability results for any size of the platoon
and understand the behaviour of the least stable pole location as the
string size increases.
All of the results obtained are illustrated by numerical examples
and ad-hoc simulations
Stability and String Stability Analysis of Formation Control Architectures for Platooning.
This thesis presents theoretical results for stability and string stability
of formation control architectures for platooning. We consider
three important interconnection topologies for vehicles travelling in a
straight line as a string: leader following, cyclic and bidirectional.
For the leader following topology we discuss modifications that allow
reduced coordination requirements. In the first case we consider
the use of the leader velocity as the state to be broadcast to the followers,
rather than the standard use of the leader position. This selection
yields a formation control architecture that achieves string stability
even under time delays in the state broadcast, while reducing typical
coordination requirements of leader following architectures. For the
second modification we change the way in which the leader position
is sent across the string to every follower. This technique keeps some
of the good transient properties of the standard leader following architecture
but eliminates most of the coordination requirements for
the followers. However, we show that this technique does not provide
string stability when time delays are present in the communication.
The second topology that we discuss is a cyclic one, where the first
member of the platoon is forced to track the last one. We discuss two
strategies: one where the inter-vehicle spacings may follow a constanttime
headway spacing policy and one where an independent leader
broadcasts its position to every member of a cyclic platoon. For both
strategies we obtain closed form expressions for the transfer functions
from disturbances to inter-vehicle spacings. These expressions allow
us to show that if the design parameters are not properly chosen, the
vehicle platoon may become unstable when the string size is greater
than a critical number. On the contrary, if the design parameters are
well chosen, both architectures can be made stable and string stable
for any size of the platoon.
The final topology that we consider is bidirectional, where every
member of the platoon, with the exception of the first and last, use
measurements of the two nearest neighbours to control their position
within the string. Although the derivations are more complex than
in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in
the form of simple transfer functions from disturbances to vehicles.
They allow us to obtain stability results for any size of the platoon
and understand the behaviour of the least stable pole location as the
string size increases.
All of the results obtained are illustrated by numerical examples
and ad-hoc simulations
Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks
This paper studies stochastic stability of a class of discrete-time
phase-coupled oscillators. We introduce the two new notions of stochastic and
ultimate stochastic phase-cohesiveness using the concepts of Harris and
positive Harris recurrent Markov chains. Stochastic phase-cohesiveness of
oscillators in two types of networks are studied. First, oscillators in a
network with an underlying connected topology subject to both multiplicative
and additive stochastic uncertainties are considered. Second, we study a
special case of the former problem by assuming that the multiplicative
uncertainties are governed by the Bernoulli process representing the well known
Erd{\H o}s R\'enyi network
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