98 research outputs found
Control of Networked Multiagent Systems with Uncertain Graph Topologies
Multiagent systems consist of agents that locally exchange information
through a physical network subject to a graph topology. Current control methods
for networked multiagent systems assume the knowledge of graph topologies in
order to design distributed control laws for achieving desired global system
behaviors. However, this assumption may not be valid for situations where graph
topologies are subject to uncertainties either due to changes in the physical
network or the presence of modeling errors especially for multiagent systems
involving a large number of interacting agents. Motivating from this
standpoint, this paper studies distributed control of networked multiagent
systems with uncertain graph topologies. The proposed framework involves a
controller architecture that has an ability to adapt its feed- back gains in
response to system variations. Specifically, we analytically show that the
proposed controller drives the trajectories of a networked multiagent system
subject to a graph topology with time-varying uncertainties to a close
neighborhood of the trajectories of a given reference model having a desired
graph topology. As a special case, we also show that a networked multi-agent
system subject to a graph topology with constant uncertainties asymptotically
converges to the trajectories of a given reference model. Although the main
result of this paper is presented in the context of average consensus problem,
the proposed framework can be used for many other problems related to networked
multiagent systems with uncertain graph topologies.Comment: 14 pages, 2 figure
Randomized Consensus with Attractive and Repulsive Links
We study convergence properties of a randomized consensus algorithm over a
graph with both attractive and repulsive links. At each time instant, a node is
randomly selected to interact with a random neighbor. Depending on if the link
between the two nodes belongs to a given subgraph of attractive or repulsive
links, the node update follows a standard attractive weighted average or a
repulsive weighted average, respectively. The repulsive update has the opposite
sign of the standard consensus update. In this way, it counteracts the
consensus formation and can be seen as a model of link faults or malicious
attacks in a communication network, or the impact of trust and antagonism in a
social network. Various probabilistic convergence and divergence conditions are
established. A threshold condition for the strength of the repulsive action is
given for convergence in expectation: when the repulsive weight crosses this
threshold value, the algorithm transits from convergence to divergence. An
explicit value of the threshold is derived for classes of attractive and
repulsive graphs. The results show that a single repulsive link can sometimes
drastically change the behavior of the consensus algorithm. They also
explicitly show how the robustness of the consensus algorithm depends on the
size and other properties of the graphs
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
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