IET Control Theory & Applications
Research Article
Consensus for multi-agent systems with
distributed adaptive control and an
event-triggered communication strategy
ISSN 1751-8644
Received on 29th November 2015
Revised on 2nd March 2016
Accepted on 16th March 2016
doi: 10.1049/iet-cta.2015.1221
www.ietdl.org
Duosi Xie
1
, Shengyuan Xu
1,
, Baoyong Zhang
1
,Yongmin Li
2
,Yuming Chu
2
1
School of Automation, Nanjing University of Science andTechnology, Nanjing 210094, People’s Republic of China
2
School of Science, HuzhouTeachers College, Huzhou 313000, People’s Republic of China
E-mail: syxu@njust.edu.cn
Abstract: This study addresses the consensus problem of multi-agent systems by combining adaptive control protocol
and event-triggered communication strategy. Two adaptive protocols are designed to guarantee the consensus. The event-
triggered communication strategy is utilised to save communication and reduce channel occupation. Each agent in the
system sends its state to neighbours only at some irregular event instants determined by an appropriately designed
event-triggering condition. At first, the distributed event-triggering condition of an agent only employs the state of its own
and the state of the neighbours at their latest event instants. Later, another event-triggering condition is given such that
no global parameter is required for agents, such as the maximum eigenvalue of the Laplacian matrix. It is proven that
the system can reach consensus by utilising the proposed control method. Illustrative examples are given to show the
effectiveness of the control strategy.
1 Introduction
Consensus problem is an attractive issue in the research of collec-
tive behaviour of multi-agent systems [1, 2]. Many researchers have
investigated this problem and gave numerous contributions [3–9].
Multi-agent systems involve a large quantity of agents that are
usually geographically distributed in a wide range. Meanwhile, the
agents communicate with each other through a wireless network.
Hence considering the physical realities that agents only have the
access to their neighbours, distributed consensus control methods
are required. An efficient approach under such situations is the
adaptive control strategy, which can adjust the control gain through
neighbours’ information [10–13]. Moreover, the channel occupa-
tion might become another issue as the communication channels
usually have bandwidth limitations. The countermeasures for these
limitations are considered in the study of sampled-data control
strategy, see [14–17] and the reference therein.
The event-triggered control strategy, as a special case of the
sampled-data strategy, has varying sampling rates. The idea of
this aperiodic scheme is that the communication among agents
happens only at irregular event instants [18–22]. The event instants
are calculated by a predefined event-triggering condition, i.e.
communication takes place when this condition is violated. The
event-triggering condition is first proposed in a centralised way
and then extended to decentralised models [23, 24]. In a general
event-triggered communication protocol, each agent samples and
sends its own state to its neighbours at its event instants. Mean-
while, each agent receives states that are sampled and sent by its
neighbours at their event instants.
Based on the aforementioned general scenario, lots of related
works have been done. Different models such as the second-order
system [25] and the general linear model [26] are considered
under such communication strategy. Beside the models, various
event-triggering protocols had also been developed. In [26], an
event-triggered communication protocol, where each agent sam-
ples both its own and neighbours’ information at its own triggering
instants, is proposed. A different event-triggering strategy, where
the agents have synchronous sampling points with a fixed time
interval, is first discussed in [27] and then extended in [28]. In their
work, each agent samples its state at the synchronous sampling
points and uses the sampled state to calculate the event-triggering
condition. If triggered, each agent sends the sampled state to its
neighbours, otherwise the agent samples its own state at the next
sampling point.
Some other works in which the event-triggered strategy has been
adopted to solve the consensus problem for the case of switching
network topologies are also considered [29, 30]. It is shown in [29]
that a sufficient condition to guarantee the event-based consensus
is to have the topology being balanced and strongly connected.
The latter part of this sufficient condition is further relaxed in
[30] such that the topology requires to be only jointly connected.
Overall, it is widely accepted that the event-triggered strategy can
be implemented into solving the consensus problem, while reduc-
ing communication times by trading the convergence rate of the
system.
In this paper, an innovative event-triggered adaptive control
protocol is proposed to solve the consensus problem in multi-
agent systems. The proposed control strategy combines dynamical
control parameter and the event-triggered communication scheme.
The dynamical adaptive parameters are designed compatible to
the consensus convergence of the system to provide agents more
flexible control gains. Other than using continuous states of neigh-
bours’, the adaptive parameter and the event-triggered control law
of an agent only involve the irregular states of neighbours that
are sampled and sent at their latest event instants. Hence the com-
munication times can be reduced by applying this event-triggered
scheme. The irregular event instants are generated by a distributed
event-triggering condition, which is state dependent. The state-
dependent strategy makes the condition relate to the convergence
states of the agents.
Moreover, the event-triggering condition does not require con-
tinuous states of neighbours either, instead it utilises the agent’s
state at the current time and its latest event time as well as its
neighbours’ states at their latest event instants. Hence no additional
communication is generated in the event calculating process.
In addition, a distributed event-triggering condition is further
proposed such that each agent does not need to have the global
information of the system like the maximum eigenvalue of the
Laplacian matrix. Instead, the agents only have the knowledge
of its own in-degree. This distributed event-triggering condition
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