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of MAS, intelligent emergence phenomena can be achieved by self-organization and internal interactions [4,5] .
As a focus of international research in related fields, the realization of consensus has profound significance in
practical applications [6–9] .

The extensive and complex application scenarios of unmanned systems make fault-tolerant control crucial.
One of the important factors contributing to the failure of unmanned systems is the damage to some individ-
ual sensor components. Huang et al. addressed the problem of IMU sensor failure by training and designing
a controller based on long short-term memory (LSTM) neural networks and datasets and proposed an AI-
based fault-tolerant control method. Furthermore, simulation verification further tested the recovery ability
and effectiveness of the design method in the above scenarios [10] . Similarly, GPS fault detection and exclu-
sion were solved by Chang and Tsai through an approach based on the moving average (MA) [11] . Compared
with traditional least-squares residual methods, their approach exhibits higher performance in detecting small
faults and similar performance levels in detecting large faults. This method has a lower incorrect exclusion rate
(IER) than traditional parity space methods and has been verified through simulation. In addition, the com-
plex communication environment of unmanned systems also poses a great challenge for consensus research,
which involves time-delay networks, random networks, asynchronous networks, etc. [12] proved the condition
for consensus in time-delay networks by introducing disagreement functions abstracted from the Lyapunov
function for the disagreement network dynamics. Based on this, Xiao et al. extended the result to variable
topology [13] . The concept of consensus in random networks was proposed by Hatano, referring to the system
converging to consensus with a probability close to 1 [14] . Asynchronous networks have been extensively stud-
ied in order to be closer to the actual situation. It is difficult to update the system state synchronously due to
the complex communication environment. The proof of the consistency of a single integral system in this sit-
uation is given by Cao et al. [15] . Recently, Yan et al. presented a distributed control protocol and a distributed
adaptive controller based on fault compensation to achieve consensus against link failures and actual/sensor
faults [16] . Moreover, Chen et al. developed an adaptive compensation protocol and an ∞ control protocol for
the scenario of simultaneous sensor or actuator faults [17] . Based on the radial basis function neural network
(RBFNN), A data-driven distributed formation control algorithm is proposed for MAS with sensor faults by
Xiong and Hou [18] .

Heterogeneous systems have also been a hot research topic in this field in recent years. Lee et al. first stud-
ied inertial systems and analyzed the impact of individual inertia indices on system consensus [19] . Using
the decomposition approach, Li and Spong investigated the stability of multiple inertial systems with non-
balanced velocity/position coupling [20] . By applying the graph theory and the Lyapunov direct method, the
consensusproblemofheterogeneoussystemscomposedoffirst-orderandsecond-orderindividualswassolved
by Zheng [21,22] . studied the consensus problem of a heterogeneous MAS consisting of quadrotors and two-
wheeled mobile robots and proposed two linear quadratic regulations (LQR)-based consensus protocols to
control the heterogeneous system, which showed good performance in practical systems. Based on the state
observers, Ma et al. solved the output consensus problem of heterogeneous MAS, which is applicable when
system states are not available [23] . By designing distributed fixed-time observers and fixed-time tracking con-
trollers, Du et al. investigated the fixed-time consensus problem for nonlinear heterogeneous systems [24] . Li
et al. further explored their research field to group consensus with input constraints [25] .

Considering the limited capabilities of sensors and processors compared to traditional communication devices
that rely on data interaction, event-triggered protocols are necessary for systems that rely on data interaction,
as they can significantly reduce the sampling frequency. Drof et al. first introduced the concept of event-
triggered and dynamically changed the system sampling frequency by measuring the state variables, which
inspired ways to reduce the system load [26] . The event-triggered threshold was correlated with the system
state by Fan et al. Their research results show that this approach has superior dynamics compared to constant
thresholds [27] . These efforts have also been gradually extended to complex systems, including heterogeneous