3,436 research outputs found
Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents
In this paper, we propose a multiplex proportional-integral approach, for
solving consensus problems in networks of heterogeneous nodes dynamics affected
by constant disturbances. The proportional and integral actions are deployed on
two different layers across the network, each with its own topology. Sufficient
conditions for convergence are derived that depend upon the structure of the
network, the parameters characterizing the control layers and the node
dynamics. The effectiveness of the theoretical results is illustrated using a
power network model as a representative example.Comment: 13 pages, 6 Figures, Preprint submitted to Automatic
Multilayer proportional-integral consensus of heterogeneous multi-agent systems
A distributed proportional-integral multilayer strategy is proposed, to achieve consensus in networks of heterogeneous first-order linear systems. The closed-loop network can be seen as an instance of so-called multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneous node dynamics. Contrary to previous approaches in the literature, the proportional and integral actions are deployed here on two different layers across the network, each with its own topology. Explicit expressions for the consensus values are obtained together with sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results are illustrated via numerical simulations using a power network example
Multilayer proportional-integral consensus of heterogeneous multi-agent systems
A distributed proportional-integral multilayer strategy is proposed, to achieve consensus in networks of heterogeneous first-order linear systems. The closed-loop network can be seen as an instance of so-called multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneous node dynamics. Contrary to previous approaches in the literature, the proportional and integral actions are deployed here on two different layers across the network, each with its own topology. Explicit expressions for the consensus values are obtained together with sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results are illustrated via numerical simulations using a power network example
Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks
We introduce a model to study the delicate relation between the spreading of
information and the formation of opinions in social systems. For this purpose,
we propose a two-layer multiplex network model in which consensus dynamics
takes place in one layer while information spreading runs across the other one.
The two dynamical processes are mutually coupled by considering that the
control parameters that govern the dynamical evolution of the state of the
nodes inside each layer depend on the dynamical states at the other layer. In
particular, we explore the scenario in which consensus is favored by the common
adoption of information while information spreading is boosted between agents
sharing similar opinions. Numerical simulations together with some analytical
results point out that, when the coupling between the dynamics of the two
layers is strong enough, a double explosive transition, i.e. an explosive
transition both for consensus dynamics and for the information spreading
appears. Such explosive transitions lead to bi-stability regions in which the
consensus-informed stated and the disagreement-ignorant states are both stable
solutions.Comment: 7 pages, 3 figure
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201
On the design of multiplex control to reject disturbances in nonlinear network systems affected by heterogeneous delays
We consider the problem of designing control protocols for nonlinear network
systems affected by heterogeneous, time-varying delays and disturbances. For
these networks, the goal is to reject polynomial disturbances affecting the
agents and to guarantee the fulfilment of some desired network behaviour. To
satisfy these requirements, we propose an integral control design implemented
via a multiplex architecture. We give sufficient conditions for the desired
disturbance rejection and stability properties by leveraging tools from
contraction theory. We illustrate the effectiveness of the results via a
numerical example that involves the control of a multi-terminal high-voltage DC
grid
Models for the modern power grid
This article reviews different kinds of models for the electric power grid
that can be used to understand the modern power system, the smart grid. From
the physical network to abstract energy markets, we identify in the literature
different aspects that co-determine the spatio-temporal multilayer dynamics of
power system. We start our review by showing how the generation, transmission
and distribution characteristics of the traditional power grids are already
subject to complex behaviour appearing as a result of the the interplay between
dynamics of the nodes and topology, namely synchronisation and cascade effects.
When dealing with smart grids, the system complexity increases even more: on
top of the physical network of power lines and controllable sources of
electricity, the modernisation brings information networks, renewable
intermittent generation, market liberalisation, prosumers, among other aspects.
In this case, we forecast a dynamical co-evolution of the smart grid and other
kind of networked systems that cannot be understood isolated. This review
compiles recent results that model electric power grids as complex systems,
going beyond pure technological aspects. From this perspective, we then
indicate possible ways to incorporate the diverse co-evolving systems into the
smart grid model using, for example, network theory and multi-agent simulation.Comment: Submitted to EPJ-ST Power Grids, May 201
Synchronization and local convergence analysis of networks with dynamic diffusive coupling
In this paper, we address the problem of achieving synchronization in networks of nonlinear units coupled by dynamic diffusive terms. We present two types of couplings consisting of a static linear term, corresponding to the diffusive coupling, and a dynamic term which can be either the integral or the derivative of the sum of the mismatches between the states of neighbouring agents. The resulting dynamic coupling strategy is a distributed proportional-integral (PI) or a proportional-derivative (PD) law that is shown to be effective in improving the network synchronization performance, for example, when the dynamics at nodes are nonidentical. We assess the stability of the network by extending the classical Master Stability Function approach to the case where the links are dynamic ones of PI/PD type. We validate our approach via a set of representative examples including networks of chaotic Lorenz and networks of nonlinear mechanical systems
- …