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CONSENSUS PROBLEM OF MULTI-AGENT SYSTEMS WITH
MARKOVIAN COMMUNICATION FAILURE
Yuebing Hu, James Lam
Department of Mechanical Engineering, University of Hong Kong, China
Jinling Liang
Department of Mathematics, Southeast University, Nanjing 210096, China
Keywords:
Consensus control, Markov chain, Mean-square stability, Communication failure, Multi-agent systems.
Abstract:
This paper studies the consensus problem of multi-agent systems with Markovian communication failure
which may be caused by limited communication capacity. The occurrence of the failures is modeled by
a discrete-time Markov chain. A consensus sufficiency condition is established in terms of linear matrix
inequalities (LMIs). Based on this condition, a new controller design method is provided. A numerical
example is utilized to illustrate the effectiveness of the proposed approach.
1 INTRODUCTION
In the past few years, multi-agent system (MAS)
has sparked the interest of researchers. Up to now,
results of networked MASs have been broadly ap-
plied to biology, physics and engineering, such as the
study of swarming behavior (Liu and Passino, 2004),
automated highway systems (AHSs) (Bender, 1991)
and congestion control in communication (Paganini
et al., 2005). In the cooperative behaviors, consensus,
which means making a group of agents to reach an
agreement on certain quantity of interest that depends
on the states of all agents, is a fundamental topic in
MASs fields and has been studied recently (Olfati-
Saber et al., 2007).
Due to the special property of MASs, the intercon-
nected communication network among agents plays
an important role in the consensus reaching problem
and is usually described by Laplacian graph. Depend-
ing on applications, the network topologies of multi-
ple agents are either fixed or switched, while the lat-
ter is more practical due to the limited or imperfect
communication channel, noises or some special ob-
jectives. Results on switching topology have been
provided in recent articles such as (Olfati-Saber and
Murray, 2004).The physical systems are usually of
big complexity, thus some dynamic processes are de-
scribed by time-varying linear model. Particularly,
for systems subject to randomly changing parameters,
Markov jump linear system (MJLS), which is a hybrid
system composed of a finite number of subsystem
modes, is an appropriate class of models and has been
extensively studied (Xiong and Lam, 2007). How-
ever, to the best of our knowledge, although MASs
are usually treated as networked systems, the issue of
Markovian topology switching processes has not been
fully investigated and fruitful results of MJLS were
not applied to MASs until now.
In this paper, we investigate the consensus control
problem of MASs with communication failure. By
modeling the communication process in a Markovian
process, a new sufficiency condition of the consensus
problem is established in terms of linear matrix in-
equalities (LMIs) which can be easily solved. Based
on this condition, a state-feedback controller is de-
signed such that the consensus of the closed-loop sys-
tem is mean square stable (MSS) with known com-
munication failure processes.
Notation. Throughout this paper, R
n
, R
n×m
, S
n×n
represent the n-dimensional Euclidean space, the set
of all n×m real matrices and the n×n real symmet-
ric positive definite matrices, respectively; Z
+
is the
set of non-negativeintegers; (Ω, F , P) denotes a com-
plete probability space; the superscript “T” represents
the transpose; for Hermitian matrices X = X
T
∈R
n×n
and Y = Y
T
∈R
n×n
, the notation X ≥Y (respectively,
X > Y) means that the matrix X −Y is positive semi-
373
Hu Y., Lam J. and Liang J. (2010).
CONSENSUS PROBLEM OF MULTI-AGENT SYSTEMS WITH MARKOVIAN COMMUNICATION FAILURE.
In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, pages 373-376
DOI: 10.5220/0002939803730376
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