Article
Event-Triggered Fixed-Time Integral Sliding Mode Control for
Nonlinear Multi-Agent Systems with Disturbances
Xue Li, Zhiyong Yu * and Haijun Jiang
Citation: Li, X.; Yu, Z.; Jiang, H.
Event-Triggered Fixed-Time Integral
Sliding Mode Control for Nonlinear
Multi-Agent Systems with
Disturbances. Entropy 2021, 23, 1412.
https://doi.org/10.3390/e23111412
Academic Editors: Luis
Hernández-Callejo, Sergio
Nesmachnow and Sara Gallardo
Saavedra
Received: 29 September 2021
Accepted: 25 October 2021
Published: 27 October 2021
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4.0/).
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;
lixuejiayouya@163.com (X.L.); jianghai@xju.edu.cn (H.J.)
* Correspondence: yzygsts@163.com or yzygsts@xju.edu.cn
Abstract:
In this paper, the leader-following consensus problem of first-order nonlinear multi-agent
systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time
sliding mode manifold is designed and a new static event-triggered protocol over general directed
graph is proposed which can well suppress the external disturbances and make the FONMASs
achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality
technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior
can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering
strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and
achieve containment control in fixed-time if the control parameters are designed carefully. Finally,
several numerical simulations are given to show the effectiveness of the proposed protocols.
Keywords: multi-agent systems; sliding mode control; leader-following consensus; fixed-time
1. Introduction
In the past several years, more and more researchers are interested in cooperative
control of multi-agent systems (MASs) because of its robustness, flexible deployment
and high efficiency. Cooperative control is widely used in various research fields to
solve engineering and non-engineering problems, such as formation of robots [
1
], sensor
networks [
2
], attitude alignment [
3
] and so on. Among multitudinous cooperative control
objectives, consensus is a basic problem in MASs. Its purpose is to design a controller which
can ensure that all members agree on an interest signal according to local information.
Therefore, the information exchange between agents on the shared network is regulated by
the consensus algorithm or protocol.
Based on observation of nature, the emergence of leaders in animal groups led to
the development of the leader-following problem in collective behavior of MASs. In the
distributed consensus problem, the existing results of MASs can be roughly divided into
three categories according to the number of leaders: leaderless consensus [
4
–
6
], leader-
following consensus [
7
–
9
] and containment control of multiple leaders [
10
,
11
]. In [
4
], the
leaderless consensus of discrete-time MASs was studied by considering the connectivity of
the network. In [
5
], the leaderless consensus of model-independent MASs was considered.
In [
6
], the leaderless consensus of fractional-order MASs was investigated. In the case of
single leader, the leader-following bipartite consensus problem was investigated for linear
MASs in [
7
]. The leader-following consensus for MASs with Lipshitz-type node dynamics
was considered in [
8
]. Furthermore, by using distributed impulsive control method, the
authors studied the leader-following consensus of nonlinear MASs in [
9
]. In the case of
multiple leaders, the reduplicative learning control problem for nonlinear heterogeneous
MASs was investigated in [
10
]. In [
11
], a completely distributed control protocol was
proposed to study the time-varying group formation tracking problem for linear MASs
with multiple leaders.
Entropy 2021, 23, 1412. https://doi.org/10.3390/e23111412 https://www.mdpi.com/journal/entropy
