1,379 research outputs found
Lyapunov Approach to Consensus Problems
This paper investigates the weighted-averaging dynamic for unconstrained and
constrained consensus problems. Through the use of a suitably defined adjoint
dynamic, quadratic Lyapunov comparison functions are constructed to analyze the
behavior of weighted-averaging dynamic. As a result, new convergence rate
results are obtained that capture the graph structure in a novel way. In
particular, the exponential convergence rate is established for unconstrained
consensus with the exponent of the order of . Also, the
exponential convergence rate is established for constrained consensus, which
extends the existing results limited to the use of doubly stochastic weight
matrices
A Chemistry-Inspired Framework for Achieving Consensus in Wireless Sensor Networks
The aim of this paper is to show how simple interaction mechanisms, inspired
by chemical systems, can provide the basic tools to design and analyze a
mathematical model for achieving consensus in wireless sensor networks,
characterized by balanced directed graphs. The convergence and stability of the
model are first proven by using new mathematical tools, which are borrowed
directly from chemical theory, and then validated by means of simulation
results, for different network topologies and number of sensors. The underlying
chemical theory is also used to derive simple interaction rules that may
account for practical issues, such as the estimation of the number of neighbors
and the robustness against perturbations. Finally, the proposed chemical
solution is validated under real-world conditions by means of a four-node
hardware implementation where the exchange of information among nodes takes
place in a distributed manner (with no need for any admission control and
synchronism procedure), simply relying on the transmission of a pulse whose
rate is proportional to the state of each sensor.Comment: 12 pages, 10 figures, submitted to IEEE Sensors Journa
Group Consensus with a Dynamic Leader for Multiagent Systems via Sampled-Data Control
This paper considers a group consensus problem with a dynamic leader for multiagent
systems in a sampled-data setting. With the leader’s state available to only
a fraction of the followers, a distributed linear protocol based on sampled-data
control is proposed for group consensus under fixed directed topology. On basis of
M-matrix theory, we derive a sufficient condition on the sampling period and the
control parameter for ultimate boundedness of the tracking errors. Furthermore,
simulation examples are provided to demonstrate the effectiveness of the theoretical
results
Recurrent Averaging Inequalities in Multi-Agent Control and Social Dynamics Modeling
Many multi-agent control algorithms and dynamic agent-based models arising in
natural and social sciences are based on the principle of iterative averaging.
Each agent is associated to a value of interest, which may represent, for
instance, the opinion of an individual in a social group, the velocity vector
of a mobile robot in a flock, or the measurement of a sensor within a sensor
network. This value is updated, at each iteration, to a weighted average of
itself and of the values of the adjacent agents. It is well known that, under
natural assumptions on the network's graph connectivity, this local averaging
procedure eventually leads to global consensus, or synchronization of the
values at all nodes. Applications of iterative averaging include, but are not
limited to, algorithms for distributed optimization, for solution of linear and
nonlinear equations, for multi-robot coordination and for opinion formation in
social groups. Although these algorithms have similar structures, the
mathematical techniques used for their analysis are diverse, and conditions for
their convergence and differ from case to case. In this paper, we review many
of these algorithms and we show that their properties can be analyzed in a
unified way by using a novel tool based on recurrent averaging inequalities
(RAIs). We develop a theory of RAIs and apply it to the analysis of several
important multi-agent algorithms recently proposed in the literature
Recurrent averaging inequalities in multi-agent control and social dynamics modeling
Many multi-agent control algorithms and dynamic agent-based models arising in
natural and social sciences are based on the principle of iterative averaging.
Each agent is associated to a value of interest, which may represent, for
instance, the opinion of an individual in a social group, the velocity vector
of a mobile robot in a flock, or the measurement of a sensor within a sensor
network. This value is updated, at each iteration, to a weighted average of
itself and of the values of the adjacent agents. It is well known that, under
natural assumptions on the network's graph connectivity, this local averaging
procedure eventually leads to global consensus, or synchronization of the
values at all nodes. Applications of iterative averaging include, but are not
limited to, algorithms for distributed optimization, for solution of linear and
nonlinear equations, for multi-robot coordination and for opinion formation in
social groups. Although these algorithms have similar structures, the
mathematical techniques used for their analysis are diverse, and conditions for
their convergence and differ from case to case. In this paper, we review many
of these algorithms and we show that their properties can be analyzed in a
unified way by using a novel tool based on recurrent averaging inequalities
(RAIs). We develop a theory of RAIs and apply it to the analysis of several
important multi-agent algorithms recently proposed in the literature
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