4,244 research outputs found
Reaching a Consensus in Networks of High-Order Integral Agents under Switching Directed Topology
Consensus problem of high-order integral multi-agent systems under switching
directed topology is considered in this study. Depending on whether the agent's
full state is available or not, two distributed protocols are proposed to
ensure that states of all agents can be convergent to a same stationary value.
In the proposed protocols, the gain vector associated with the agent's
(estimated) state and the gain vector associated with the relative (estimated)
states between agents are designed in a sophisticated way. By this particular
design, the high-order integral multi-agent system can be transformed into a
first-order integral multi-agent system. And the convergence of the transformed
first-order integral agent's state indicates the convergence of the original
high-order integral agent's state if and only if all roots of the polynomial,
whose coefficients are the entries of the gain vector associated with the
relative (estimated) states between agents, are in the open left-half complex
plane. Therefore, many analysis techniques in the first-order integral
multi-agent system can be directly borrowed to solve the problems in the
high-order integral multi-agent system. Due to this property, it is proved that
to reach a consensus, the switching directed topology of multi-agent system is
only required to be "uniformly jointly quasi-strongly connected", which seems
the mildest connectivity condition in the literature. In addition, the
consensus problem of discrete-time high-order integral multi-agent systems is
studied. The corresponding consensus protocol and performance analysis are
presented. Finally, three simulation examples are provided to show the
effectiveness of the proposed approach
Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization
Most of the distributed protocols for multi-agent consensus assume that the
agents are mutually cooperative and "trustful," and so the couplings among the
agents bring the values of their states closer. Opinion dynamics in social
groups, however, require beyond these conventional models due to ubiquitous
competition and distrust between some pairs of agents, which are usually
characterized by repulsive couplings and may lead to clustering of the
opinions. A simple yet insightful model of opinion dynamics with both
attractive and repulsive couplings was proposed recently by C. Altafini, who
examined first-order consensus algorithms over static signed graphs. This
protocol establishes modulus consensus, where the opinions become the same in
modulus but may differ in signs. In this paper, we extend the modulus consensus
model to the case where the network topology is an arbitrary time-varying
signed graph and prove reaching modulus consensus under mild sufficient
conditions of uniform connectivity of the graph. For cut-balanced graphs, not
only sufficient, but also necessary conditions for modulus consensus are given.Comment: scheduled for publication in IEEE Transactions on Automatic Control,
2016, vol. 61, no. 7 (accepted in August 2015
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
Consensus analysis of multi-agent systems under switching topologies by a topology-dependent average dwell time approach
© The Institution of Engineering and Technology 2016. This study addresses the consensus problem for a class of any order multi-agent systems under switching topologies which could include kinds of unconsensusable topologies. The consensus problem, depending on structure properties and the corresponding topology, is researched with fixed structure properties under directed switching topologies. By the properties of Laplacian matrix, the consensus problem for multi-agent systems is converted into the stability problem of the corresponding switched systems with a Laplacian-like matrix. Some sufficient conditions for consensus are presented by using the dwell time approach. Finally, numerical examples and the results of computer simulation are given to verify the theoretical analysis
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