Adaptive Event-Triggered Consensus Control for Multi-Agent Systems
Subject to Input Saturation
Xiuxia Yin, Dong Yue and Songlin Hu
Abstract— This paper investigates the distributed adaptive
event-triggered consensus control for a class of Lipschitz nonlin-
ear agents. Each agent is subject to input saturation. Two kinds
of distributed event-triggered control scheme are introduced,
one is continuous-time based event-triggered scheme and the
other is sampled-data based event-triggered scheme. Compared
with the traditional event-triggered schemes in the existing
literatures, the parameters of the event-triggered schemes in
this paper are adaptively adjusted by using some event-error-
dependent adaptive laws. The problem of simultaneously deriv-
ing the event-triggered controllers and tackling the saturation
nonlinearity is cast into standard linear matrix inequalities
problem. A convincing simulation example is given to demon-
strate the theoretical results.
Key words: multi-agent systems, input saturation, adaptive,
event-triggered, LMI.
I. INTRODUCTION
For a decade, the consensus problem for multi-agent
systems (MASs) has been studied extensively by various sci-
enti¿c communities, due to its broad applications in robots,
formation control of unmanned air vehicles, sensor networks
and so on [1]. Consensus requires all agents to achieve a
desired common goal using only neighboring information
[2]. Until now, the existing works about consensus are mainly
focus on the single-integrator dynamics or double-integrator
kinematics or fractional-order kinematics [3], [4], [5] , while
some other authors have studied the consensus problem for
high-order linear models [2]. Leader-following approach is
commonly adopted by researchers to help agents arrive at
the desired destination.
For a multi-agent system, each agent can be controlled by
an embedded micro-processor who is used to gather infor-
mation from neighboring agents. Information among agents
is transmitted through communication networks. In practice,
communication networks, especially wireless networks, have
bandwidth limitations that may cause d e lays or disorders in
message delivery. Such limitations may seriously degrade the
system’s stability performance. To solve this commu nication
issue, event-triggering control strategy has been drawn an
increasing attention in more recent years for its bene¿ts
in saving the communication resources and reducing the
communication burden [2], [6], [7], [8]. This is done by
having agents broadcast their state information signals only
in the case of occurrence of local events that are triggered
Dong Yue and Songlin Hu are with the Institute of Advanced Technology,
Nanjing Univ e rsity of Posts and Telecommunications, Nanjing, Jiangsu,
P.R.China.
medongy@vip.163.com.
Xiuxia Yin is with the Department of Mathematics, School of Science,
Nanchang University, Nanchang, 330031, P.R. China.
depending on some predesigned rulings. However, this novel
control strategy has not been studied extensively for MASs
with general lin ear models.
Motivated by the above mentions and also taking into
account that in real control systems, the actuators have often
been subject to saturation owing to some physical limitations
[9], [10], [11]. For example, the ability of each robot to adjust
its orientation for achieving the desired formation is limited.
In this paper, we study the consensus problem for nonlinear
MASs with general models and input saturation based on
the event-triggered communication scheme, which has not
been investigated before. To study this problem is not only
theoretically challenging but also practically imperative.
It will be shown that all agents in the group with a
virtual leader can reach the leader-following consensus when
only a subgroup of the agents can access to the leader’s
state information. Since the introduction of the adaptive
mechanism in the event-trigger’s parameters, the dif¿culties
in choosing suitable initial parameters will be avoided. The
controller gain and the event-triggering parameter can be co-
designed in terms of LMI techniques.
II. P
RELIMINARIES AND SYSTE M MODE L
The directed algebraic graph theory is important and basic
for us to investigate this paper, one can see refs. [4], [5].
The multi-agent system consid ered in this paper consists
of N following agents indexed by 1, 2,...N and a virtual
leader indexed by 0. Each agent is d escribed by
˙x
i
(t)=Ax
i
(t)+f(x
i
(t),t)+Bσ(u
i
(t)) (1)
˙x
0
(t)=Ax
0
(t)+f(x
0
(t),t) (2)
where x
i
(t) ∈ R
n
and u
i
(t) ∈ R
p
denote the state
and control input of the ith agent, f(x
i
(t),t) ∈ R
n
is its nonlinear dynamics, σ : R
p
→ R
p
is a saturation function de¿ned as σ(u
i
)=
[
sat(u
i1
) sat(u
i2
) ··· sat(u
ip
)
]
T
, sat(u
ij
)=
sgn(u
ij
)min{|u
ij
| ,u
0
} for some constant u
0
> 0.A
and B are constant matrices with suitable dimensions.
x
0
is the leader with f(x
0
(t),t) be its intrinsic nonlinear
dynamics. The initial conditions are x
i
(0).i∈ S
N
∪{0}.
S
N
{1, 2,...,N}.
Assumption 1: [12] The nonlinear function f : R
n
→ R
n
satis¿es the Lipschitz condition, i.e.,
∃l>0, s.t., f(x) − f(y) <l x − y (3)
for any x, y ∈ R
n
.
Assumption 2: The communication network has a directed
spanning tree.
Proceedings of the 34th Chinese Control Conference
Jul
28-30, 2015, Han
zhou, China
7245