www.ietdl.org
Published in IET Control Theory and Applications
Received on 31st August 2013
Revised on 25th July 2014
Accepted on 5th August 2014
doi: 10.1049/iet-cta.2013.1117
ISSN 1751-8644
Connection-graph-based event-triggered output
consensus in multi-agent systems with
time-varying couplings
Xu Zhang, Maoyin Chen, Ling Wang, Zhonghua Pang, Donghua Zhou
Department of Automation,Tsinghua University, Beijing 100084, People’s Republic of China
E-mail: mychen@mail.tsinghua.edu.cn
Abstract: Event-triggered strategies are effective to update local controllers in multi-agent systems (MASs) at necessary
discrete times. Based on graph theoretical reasoning, the authors study the distributed event-triggered output consensus in
MASs with time-varying couplings. Graph theoretical reasoning provides us a Lyapunov function that fully utilises the
properties of a graph such as the path between two arbitrary agents. With this function, the updating of local output-feedback
controllers is determined by connection-graph-based state-dependent or time-dependent event functions. Interesting enough,
the proposed event-triggered schemes can also be effectively extended to non-linear MASs with time-varying couplings.
Theoretical analysis and numerical simulations verify the main results.
1 Introduction
Multi-agent systems (MASs) have attracted much attention
in many areas including vehicles [1], flocking [2], formation
[3] and sensor networks [4]. One main issue is the consen-
sus, that is, how to make each agent reach agreement on
certain quantities of interest [5–9]. Some fundamental works
are presented for linear MASs with fixed and switching
topologies [5] and for double-integrator agents [6]. In prac-
tical cases, because of limited resource, agents communicate
with each other only at discrete times, and a discrete-time
protocol may be necessary. Discrete-time updating schemes
are proposed in [7], where agents have a common sam-
pling period and communicate in a periodical pattern. In
[8], sampled-data-based consensus is considered, where a
queuing mechanism makes all agents update their control
inputs synchronously. For agents with asynchronous updat-
ing times, a distributed consensus protocol is proposed using
local information [9].
Generally speaking, there are two main ways to update
controllers in the discrete-time protocol, that is, time-driven
and event-driven. Although the former is easy to design,
it may lead to excessive usage of resource for embedded
control systems and be difficult to carry out with commu-
nication time delays [10, 11]. The sampling times for the
latter are decided by triggering pre-designed events, which
reduces ‘unnecessary’ samplings [12]. A detailed summary
on event-triggered sampling can be found in [13, 14] and
comparison of two controller updating patterns for stochastic
systems can be found in [15, 16].
In the literature, the event-triggered consensus for a first-
order MAS is discussed [12, 17–19]. In [17], both the
centralised and distributed schemes are considered, where
controllers are updated depending on a triggering function.
The results are extended to a self-triggered setup [12], where
each agent computes the next updating time at the previous
one. In order to reduce the updating, Fan et al.[18] designed
a different event function based on which the control pro-
tocol of each agent is updated only at its own event times.
Based on a distributed event-triggered control protocol, the
work [20] solves robust consensus in non-linear MASs. In
general, the threshold for event-triggered function can be
state-dependent and time-dependent. In the former case, the
MASs achieve consensus asymptotically but may face higher
frequency of controller updates when the number of agents
is large. In the latter case, the convergence rate is determined
by some external signals [20, 21].
Until now, the works on event-triggered consensus have
the following limitations. On the one hand, most works only
consider event-triggered state consensus in MASs with time-
invariant couplings. In practical cases, such as a swarm of
vehicles in uncertain environments, the coupling between
two vehicles may be time-varying because of the time-
varying distance between each other. In addition, full states
of agent may not be known, and output consensus is nec-
essary. On the other hand, some works only consider linear
MASs, where first-order or second-order MASs are often
studied. As far as we know, there exist scarce works con-
sidering the event-triggered state consensus in non-linear
MASs, not to mention the output consensus.
Inspired by graph theoretical reasoning [22], we study
the event-triggered output consensus in MASs with time-
varying couplings. Using the properties of communication
topology such as the path between two arbitrary agents, both
state-dependent and time-dependent event-triggered strate-
gies are designed. Although the state-dependent triggering
IET Control Theory Appl., 2015, Vol. 9, Iss. 1, pp. 1–9 1
doi: 10.1049/iet-cta.2013.1117 © The Institution of Engineering and Technology 2014