2,732 research outputs found
Convergence Tools for Consensus in Multi-Agent Systems with Switching Topologies
We present two main theorems along the lines of Lyapunov's second method that
guarantee asymptotic state consensus in multi-agent systems of agents in R^m
with switching interconnection topologies. The two theorems complement each
other in the sense that the first one is formulated in terms of the states of
the agents in the multi-agent system, whereas the second one is formulated in
terms of the pairwise states for each pair of agents in the multi-agent system.
In the first theorem, under the assumption that the interconnection topology is
uniformly strongly connected and the agents are contained in a compact set, a
strong form of attractiveness of the consensus set is assured. In the second
theorem, under the weaker assumption that the interconnection topology is
uniformly quasi strongly connected, the consensus set is guaranteed to be
uniformly asymptotically stable.Comment: 28 pages, 3 figure
Multi-Agent Distributed Coordination Control: Developments and Directions
In this paper, the recent developments on distributed coordination control,
especially the consensus and formation control, are summarized with the graph
theory playing a central role, in order to present a cohesive overview of the
multi-agent distributed coordination control, together with brief reviews of
some closely related issues including rendezvous/alignment, swarming/flocking
and containment control.In terms of the consensus problem, the recent results
on consensus for the agents with different dynamics from first-order,
second-order to high-order linear and nonlinear dynamics, under different
communication conditions, such as cases with/without switching communication
topology and varying time-delays, are reviewed, in which the algebraic graph
theory is very useful in the protocol designs, stability proofs and converging
analysis. In terms of the formation control problem, after reviewing the
results of the algebraic graph theory employed in the formation control, we
mainly pay attention to the developments of the rigid and persistent graphs.
With the notions of rigidity and persistence, the formation transformation,
splitting and reconstruction can be completed, and consequently the range-based
formation control laws are designed with the least required information in
order to maintain a formation rigid/persistent. Afterwards, the recent results
on rendezvous/alignment, swarming/flocking and containment control, which are
very closely related to consensus and formation control, are briefly
introduced, in order to present an integrated view of the graph theory used in
the coordination control problem. Finally, towards the practical applications,
some directions possibly deserving investigation in coordination control are
raised as well.Comment: 28 pages, 8 figure
Leader-following Consensus Problems with a Time-varying Leader under Measurement Noises
In this paper, we consider a leader-following consensus problem for networks
of continuous-time integrator agents with a time-varying leader under
measurement noises. We propose a neighbor-based state-estimation protocol for
every agent to track the leader, and time-varying consensus gains are
introduced to attenuate the noises. By combining the tools of stochastic
analysis and algebraic graph theory, we study mean square convergence of this
multi-agent system under directed fixed as well as switching interconnection
topologies. Sufficient conditions are given for mean square consensus in both
cases. Finally, a numerical example is given to illustrate our theoretical
results.Comment: 12 pages 3 figure
Containment control of multi-agent systems with measurement noises
In this paper, containment control of multi-agent systems with measurement
noises is studied under directed networks. When the leaders are stationary, a
stochastic approximation type protocol is employed to solve the containment
control of multi-agent systems. By using stochastic analysis tools and
algebraic graph theory, some necessary and sufficient criteria are established
to ensure the followers converge to the convex hull spanned by the leaders in
the sense of mean square and probability 1. When the leasers are dynamic, a
stochastic approximation type protocol with distributed estimators is developed
and necessary and sufficient conditions are also obtained for solving the
containment control problem. Simulations are provided to illustrate the
effectiveness of the theoretical results.Comment: 8 page
Connectivity and Set Tracking of Multi-agent Systems Guided by Multiple Moving Leaders
In this paper, we investigate distributed multi-agent tracking of a convex
set specified by multiple moving leaders with unmeasurable velocities. Various
jointly-connected interaction topologies of the follower agents with
uncertainties are considered in the study of set tracking. Based on the
connectivity of the time-varying multi-agent system, necessary and sufficient
conditions are obtained for set input-to-state stability and set integral
input-to-state stability for a nonlinear neighbor-based coordination rule with
switching directed topologies. Conditions for asymptotic set tracking are also
proposed with respect to the polytope spanned by the leaders
Secure and Privacy Preserving Consensus for Second-order Systems Based on Paillier Encryption
This paper aims at secure and privacy preserving consensus algorithms of
networked systems. Due to the technical challenges behind decentralized design
of such algorithms, the existing results are mainly restricted to a network of
systems with simplest first-order dynamics. Like many other control problems,
breakthrough of the gap between first-order dynamics and higher-order ones
demands for more advanced technical developments. In this paper, we explore a
Paillier encryption based average consensus algorithm for a network of systems
with second-order dynamics, with randomness added to network weights. The
conditions for privacy preserving, especially depending on consensus rate, are
thoroughly studied with theoretical analysis and numerical verification
Dynamic Average Consensus under Limited Control Authority and Privacy Requirements
This paper introduces a novel continuous-time dynamic average consensus
algorithm for networks whose interaction is described by a strongly connected
and weight-balanced directed graph. The proposed distributed algorithm allows
agents to track the average of their dynamic inputs with some steady-state
error whose size can be controlled using a design parameter. This steady-state
error vanishes for special classes of input signals. We analyze the asymptotic
correctness of the algorithm under time-varying interaction topologies and
characterize the requirements on the stepsize for discrete-time
implementations. We show that our algorithm naturally preserves the privacy of
the local input of each agent. Building on this analysis, we synthesize an
extension of the algorithm that allows individual agents to control their own
rate of convergence towards agreement and handle saturation bounds on the
driving command. Finally, we show that the proposed extension additionally
preserves the privacy of the transient response of the agreement states and the
final agreement value from internal and external adversaries. Numerical
examples illustrate the results.Comment: 44 page
Random consensus in nonlinear systems under fixed topology
This paper investigates the consensus problem in almost sure sense for
uncertain multi-agent systems with noises and fixed topology. By combining the
tools of stochastic analysis, algebraic graph theory, and matrix theory, we
analyze the convergence of a class of distributed stochastic type non-linear
protocols. Numerical examples are given to illustrate the results.Comment: 9 pages, 5 figures. arXiv admin note: text overlap with
arXiv:0909.316
Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays
In this paper, we study asynchronous consensus problems of continuous-time
multi-agent systems with discontinuous information transmission. The proposed
consensus control strategy is implemented only based on the state information
at some discrete times of each agent's neighbors. The asynchronization means
that each agent's update times, at which the agent adjusts its dynamics, are
independent of others'. Furthermore, it is assumed that the communication
topology among agents is time-dependent and the information transmission is
with bounded time-varying delays. If the union of the communication topology
across any time interval with some given length contains a spanning tree, the
consensus problem is shown to be solvable. The analysis tool developed in this
paper is based on the nonnegative matrix theory and graph theory. The main
contribution of this paper is to provide a valid distributed consensus
algorithm that overcomes the difficulties caused by unreliable communication
channels, such as intermittent information transmission, switching
communication topology, and time-varying communication delays, and therefore
has its obvious practical applications. Simulation examples are provided to
demonstrate the effectiveness of our theoretical results.Comment: Regular pape
Average Consensus on General Strongly Connected Digraphs
We study the average consensus problem of multi-agent systems for general
network topologies with unidirectional information flow. We propose two
(linear) distributed algorithms, deterministic and gossip, respectively for the
cases where the inter-agent communication is synchronous and asynchronous. Our
contribution is that in both cases, the developed algorithms guarantee state
averaging on arbitrary strongly connected digraphs; in particular, this
graphical condition does not require that the network be balanced or symmetric,
thereby extending many previous results in the literature. The key novelty of
our approach is to augment an additional variable for each agent, called
"surplus", whose function is to locally record individual state updates. For
convergence analysis, we employ graph-theoretic and nonnegative matrix tools,
with the eigenvalue perturbation theory playing a crucial role
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