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Page 2 of 13 Ding et al. Complex Eng Syst 2023;3:7 I http://dx.doi.org/10.20517/ces.2023.06

1. INTRODUCTION
As typical autonomous cyber-physical systems, multi-agent systems (MASs) provide an effective means to
coordinate spatially distributed and networked agents, where agents interact together to optimize decisions
and achieve system objectives. In recent decades, the development of cluster control has motivated more and
more research on the consensus problem for MASs, such as multi-UAVs (Unmanned Aerial Vehicles) con-
[4]
[9]
trol [1–3] , underwater cooperative operations , robot formation control [5–8] , wireless sensors collaboration ,
microgrids control [10] and so on. As a key issue in the research of MASs, the consensus problem has received
extensive attention in the past few decades. For example, Hu et al. proposed a new consensus protocol for
complex networks composed of multiple subnetworks to ensure convergence [11] . Yao et al. considered the
finite-time consensus problem of MASs based on the finite-time Lyapunov stability theory [12] . Rehman et
al. investigated the consensus problem of leader-following MASs in both fixed undirected topology and fixed
directed topology and proposed two distributed control protocols [13] . Liu et al. studied the positive consensus
problem of MASs with directed communication topologies where all agents have identical continuous-time
positive linear dynamics [14] .

To handle the consensus problem, various control methods have been proposed including fuzzy control [15] ,
robust ∞ control [16] , predictive control [17,18] , adaptive control [19–21] , sliding mode control (SMC) [22] , and
so on. Due to the strong robustness to external disturbance and parameter uncertainties, the sliding mode
control method has been used widely in the MASs consensus research. For the leaderless MASs, Wang et al.
designed a special SMC protocol for the consensus problem [23] . Cong et al. proposed a distributed nonsingu-
lar controller to deal with the consensus problem for a class of nonlinear single-integrator MASs with input
uncertain dynamics [24] . Rahmani et al. proposed a projection recurrent neural network, which was suitable
for robotic MASs, and designed a new optimal SMC technique to achieve consensus tracking [25] .

However, a key feature of the aforementioned works is that the information can be transmitted accurately
among agents. In practical MASs, a satisfying communication environment cannot be guaranteed under wire-
less transmission networks. As a result of the impact of amplitude attenuation and random interference, the
wireless link communication among agents will suffer from the fading phenomenon, resulting in the distor-
tion of the data. This unfavorable factor motivated some interesting research on consensus tracking of wireless
MASs subject to channel fading. Oral et al. [26] considered link outages between agents and obtained the prob-
ability expression for MASs reaching consensus. Gu et al. designed a distributed SMC law to deal with the
impact of the information fading phenomenon in communication channels [27] . Ding et al. investigated the
finite-time consensus control for MASs with channel fading via SMC technique. [28]

Another adverse phenomenon in the wireless transmission network is the inevitable malicious attacks, thereby
rendering the secure control of MASs fundamental significance [29] . Considering the different mechanisms
and effects on the MASs consensus problem, cyber-attacks can be divided into various types, for example,
deception attacks [30] , replay attacks [31] and denial-of-service (DoS) attacks [32] . Among them, deception at-
tacks may lead to erroneous information feedback by tampering with the real packets via injecting false data.
Cui et al. investigated the consensus tracking problem of MASs, which may be subject to deception attacks
randomly. Recently, SMC strategy combined with adaptive mechanism has shown promising performance
for constrained systems, for example, Chen et al. constructed an adaptive sliding mode control law to deal
with the effects of adversarial cyber injection attacks [33] . It is of great practical significance to investigate the
consensus problem for MASs against deception attacks [34] . Meanwhile, it is challenging to design a feasible
SMC law under unknown and time-varying deception attacks.

Inspired by the above discussion and based on the expanded research of ref. [28] , this paper will be concerned
with the secure consensus control problem for multi-agent systems with malicious attacks and channel fading
via the adaptive sliding mode technique, and the main contributions are highlighted as follows: (1) Both the