429 research outputs found
Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology
This paper studies the local and global exponential synchronization of a complex dynamical network with switching topology and time-varying coupling delays. By using stability theory of switched systems and the network topology, the synchronization of such a network under some special switching signals is investigated. Firstly, under the assumption that all subnetworks are self-synchronizing, a delay-dependent sufficient condition is given in terms of linear matrix inequalities, which guarantees the solvability of the local synchronization problem under an average dwell time scheme. Then this result is extended to the situation that not all subnetworks are self-synchronizing. For the latter case, in addition to average dwell time, an extra condition on the ratio of the total activation time of self-synchronizing and nonsynchronizing subnetworks is needed to achieve synchronization of the entire switched network. The global synchronization of a network whose isolate dynamics is of a particular form is also studied. Three different examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results. © 2006 IEEE.published_or_final_versio
Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling
Distributed algorithms of multi-agent coordination have attracted substantial
attention from the research community; the simplest and most thoroughly studied
of them are consensus protocols in the form of differential or difference
equations over general time-varying weighted graphs. These graphs are usually
characterized algebraically by their associated Laplacian matrices. Network
algorithms with similar algebraic graph theoretic structures, called being of
Laplacian-type in this paper, also arise in other related multi-agent control
problems, such as aggregation and containment control, target surrounding,
distributed optimization and modeling of opinion evolution in social groups. In
spite of their similarities, each of such algorithms has often been studied
using separate mathematical techniques. In this paper, a novel approach is
offered, allowing a unified and elegant way to examine many Laplacian-type
algorithms for multi-agent coordination. This approach is based on the analysis
of some differential or difference inequalities that have to be satisfied by
the some "outputs" of the agents (e.g. the distances to the desired set in
aggregation problems). Although such inequalities may have many unbounded
solutions, under natural graphic connectivity conditions all their bounded
solutions converge (and even reach consensus), entailing the convergence of the
corresponding distributed algorithms. In the theory of differential equations
the absence of bounded non-convergent solutions is referred to as the
equation's dichotomy. In this paper, we establish the dichotomy criteria of
Laplacian-type differential and difference inequalities and show that these
criteria enable one to extend a number of recent results, concerned with
Laplacian-type algorithms for multi-agent coordination and modeling opinion
formation in social groups.Comment: accepted to Automatic
Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels
In this paper we propose and analyze a distributed algorithm for achieving
globally optimal decisions, either estimation or detection, through a
self-synchronization mechanism among linearly coupled integrators initialized
with local measurements. We model the interaction among the nodes as a directed
graph with weights (possibly) dependent on the radio channels and we pose
special attention to the effect of the propagation delay occurring in the
exchange of data among sensors, as a function of the network geometry. We
derive necessary and sufficient conditions for the proposed system to reach a
consensus on globally optimal decision statistics. One of the major results
proved in this work is that a consensus is reached with exponential convergence
speed for any bounded delay condition if and only if the directed graph is
quasi-strongly connected. We provide a closed form expression for the global
consensus, showing that the effect of delays is, in general, the introduction
of a bias in the final decision. Finally, we exploit our closed form expression
to devise a double-step consensus mechanism able to provide an unbiased
estimate with minimum extra complexity, without the need to know or estimate
the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin
Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks
In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud
and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm
Decentralised adaptive control of a class of hidden leader–follower non-linearly parameterised coupled MASs
In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme
On fast-slow consensus networks with a dynamic weight
We study dynamic networks under an undirected consensus communication
protocol and with one state-dependent weighted edge. We assume that the
aforementioned dynamic edge can take values over the whole real numbers, and
that its behaviour depends on the nodes it connects and on an extrinsic slow
variable. We show that, under mild conditions on the weight, there exists a
reduction such that the dynamics of the network are organized by a
transcritical singularity. As such, we detail a slow passage through a
transcritical singularity for a simple network, and we observe that an exchange
between consensus and clustering of the nodes is possible. In contrast to the
classical planar fast-slow transcritical singularity, the network structure of
the system under consideration induces the presence of a maximal canard. Our
main tool of analysis is the blow-up method. Thus, we also focus on tracking
the effects of the blow-up transformation on the network's structure. We show
that on each blow-up chart one recovers a particular dynamic network related to
the original one. We further indicate a numerical issue produced by the slow
passage through the transcritical singularity
Synchronization and Noise: A Mechanism for Regularization in Neural Systems
To learn and reason in the presence of uncertainty, the brain must be capable
of imposing some form of regularization. Here we suggest, through theoretical
and computational arguments, that the combination of noise with synchronization
provides a plausible mechanism for regularization in the nervous system. The
functional role of regularization is considered in a general context in which
coupled computational systems receive inputs corrupted by correlated noise.
Noise on the inputs is shown to impose regularization, and when synchronization
upstream induces time-varying correlations across noise variables, the degree
of regularization can be calibrated over time. The proposed mechanism is
explored first in the context of a simple associative learning problem, and
then in the context of a hierarchical sensory coding task. The resulting
qualitative behavior coincides with experimental data from visual cortex.Comment: 32 pages, 7 figures. under revie
Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching
This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist of κ modes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employing M-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results
- …