Consensus of first-order multi-agent systems with
intermittent interaction
Yanping Gao
a
, Bo Liu
b,
n
, Junyan Yu
c
, Jingwei Ma
d,e
, Tongqiang Jiang
a
a
College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China
b
College of Sciences, North China University of Technology, Beijing 100144, China
c
College of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China
d
Department of Automation, Tsinghua University, Beijing 100084, China
e
Naval Aeronautical Engineering University, Yantai 264000, China
article info
Article history:
Received 16 April 2013
Received in revised form
30 July 2013
Accepted 15 September 2013
Communicated by D. Liu
Available online 16 November 2013
Keywords:
Multi-agent systems
First-order agents
Consensus
Intermittent interaction
abstract
This paper studies the consensus problem of multiple agents with continuous-time first-order dynamics,
where each agent can only obtain its states relative to its neighbors at sampling instants. It is assumed
that the sampling period is different from the period of zero-order hold. Some sufficient and necessary
conditions for consensus, which reveal the relationship among the interaction topology, controller
gains, and the periods of sampler and zero-order hold, are provided. Moreover, the convergence rate is
compared with that in the case when the period of zero-order hold is the same as the sampling period.
Simulations are performed to validate the theoretical results.
& 2013 Elsevier B.V. All rights reserved.
1. Introduction
In many coordinated control problems, a critical issue is to
design appropriate controllers such that all agents reach an
agreement on certain quantities of interest, which may be the
formation center in formation control, the expected attitude in
attitude alignment, or the destination in rendezvous problem.
Such a problem is called consensus problem [1,2].
Many researchers have investigated consensus from different
viewpoints, such as the dynamics of agents, the interaction
topology and information transmission among agents, the con-
vergence rate and so on. In [3], consensus of heterogeneous multi-
agent systems is addressed, where some agents are with first-
order dynamics and the others are with second-order dynamics. In
[4], leader-following consensus is studied for second-order non-
linear multi-agent systems via pinning control. Output feedback
consensus is considered for multi-agent systems with general
linear continuous-time dynamics in [5], and consensus of multiple
agents with high-order dynamics is considered in [6]. Consensus
of second-order and first-order multi-agent systems with time-
varying topology is studied in [7,8], respectively. In [9], the
interaction among agents is modeled as a random graph and
mean-square consensus is investigated. In [10–12], asynchronous
consensus, i.e., the time when each agent updates its control input
is independent of the others', is analyzed. In [13], finite-time
consensus of first-order multi-agent systems is studied by apply-
ing the theory of finite-time stability theory, and in [14], finite-
time consensus of multi-agent systems composed of single-
integrators and double-integrators is addressed.
Due to the limitation of bandwidth, the cost of communication,
and the technique constraints, etc, it is possible to transmit
information among agents in the intermittent manner. Hence,
consensus of continuous-time multi-agent systems with intermit-
tent interaction has received more and more attention recently.
In [15], consensus of first-order multi-agent systems is considered
in the cases with sampling delay and without sampling delay,
respectively, and some sufficient and necessary conditions are
provided in the case of fixed topology. In [16,17], sufficient and
necessary conditions are provided for second-order multi-agent
systems with periodic sampling. In [18,19], consensus is analyzed
for second-order multi-agent systems with time-varying sampling
intervals by applying matrix theory and Lyapunov stability theory,
respectively. It should be mentioned that the above results are
based on the following assumption: the sampling time is the same
as the update time of zero-order hold, namely, each agent obtains
the information from its neighbors and updates its control input at
the same time. However, in some practical situations, the sampling
time and the update time of zero-order hold may be different
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/neucom
Neurocomputing
0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.neucom.2013.09.031
n
Corresponding author.
E-mail addresses: gaoyanping@pku.edu.cn (Y. Gao), boliu@ncut.edu.cn (B. Liu).
Neurocomputing 129 (2014) 273–278
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