## 4 Simulation Results  
The communication topology \(\mathcal{G}\) of the control scheme is shown in Figure 2.  
To validate the proposed control method's effectiveness, the first numerical simulation is carried out using a three-motor simulation system [22], and the specific experimental parameters are set as follows:  
\[A_{1}=\left[ \begin{array}{ccc}1.2998&-0.4341&0.1343\\ 1&0&0\\ 0&1&0\end{array} \right],B_{1}=\left[ \begin{array}{c}1\\ 0\\ 0\end{array} \right],\]  
\[C_{1}=\left[ \begin{array}{ccc}3.5629&2.7739&1.0121\end{array} \right],F_{1} =B_{1},\]  
\[A_{2}=\left[ \begin{array}{ccc}1.1993&-0.4101&0.1273\\ 1&0&0\\ 0&1&0\end{array} \right],B_{2}=\left[ \begin{array}{c}1\\ 0\\ 0\end{array} \right],\]  
Figure 2: Communication topology \(\mathcal{G}\). \[C_{2}=\left[ \begin{array}{ccc}3.3652&2.4369&0.9271\end{array} \right],F_{2}=B_{2},\]  
\[A_{3}=\left[ \begin{array}{ccc}1.0785&-0.4413&0.1385\\ 1&0&0\\ 0&1&0\end{array} \right],B_{3}=\left[ \begin{array}{c}1\\ 0\\ 0\end{array} \right],\]  
\[C_{3}=\left[ \begin{array}{ccc}3.2519&2.2984&1.0213\end{array} \right],F_{3}= B_{3}.\]  
\[A_{4}=\left[ \begin{array}{ccc}1.0921&-0.4018&0.1421\\ 1&0&0\\ 0&1&0\end{array} \right],B_{4}=\left[ \begin{array}{c}1\\ 0\\ 0\end{array} \right],\]  
\[C_{4}=\left[ \begin{array}{ccc}3.0126&2.1172&0.9837\end{array} \right],F_{4}= B_{4}.\]  
The controller gains of the agents are designed as follows:  
\[L_{1}^{\text{a}}=\left[ \begin{array}{ccc}0.1781&-0.0327&0.0935&-0.0061\end{array} \right],\]  
\[L_{2}^{\text{a}}=\left[ \begin{array}{ccc}0.0769&-0.0087&0.0865&-0.0067\end{array} \right],\]  
\[L_{3}^{\text{a}}=\left[ \begin{array}{ccc}-0.0437&-0.0391&0.0977&-0.0068\end{array} \right],\]  
\[L_{4}^{\text{a}}=\left[ \begin{array}{ccc}-0.0300&0.0006&0.1013&-0.0073\end{array} \right],\]  
\[L_{1}^{\text{b}}=L_{2}^{\text{b}}=L_{3}^{\text{b}}=L_{4}^{\text{b}}=0.005,\]  
\[a_{12}=a_{14}=a_{21}=a_{23}=a_{32}=a_{34}=a_{41}=a_{43}=1,\]  
\[a_{13}=a_{24}=a_{31}=a_{42}=0,\]  
\[W_{1}=W_{2}=W_{3}=W_{4}=5,\]  
\[N_{1}=N_{2}=N_{3}=N_{4}=I,\]  
\[\eta_{1}=\eta_{2}=\eta_{3}=\eta_{4}=0.5*10^{-7},\]  
\[\tau_{t,1}^{\text{ca}}\in\left[1\,3\right],\tau_{t,2}^{\text{ca}}\in\left[0\, 3\right],\tau_{t,3}^{\text{ca}}\in\left[1\,2\right],\tau_{t,4}^{\text{ca}}\in \left[1\,3\right],\]  
\[\tau_{t,1}^{\text{sc}}\in\left[1\,3\right],\tau_{t,2}^{\text{sc}}\in\left[1\, 2\right],\tau_{t,3}^{\text{sc}}\in\left[0\,2\right],\tau_{t,4}^{\text{sc}}\in \left[0\,3\right].\]  
At 8 s, the leader encountered an actuator fault, and the fault is set as follows:  
\[f_{1}(t)= \begin{cases}0,&t<200\\ 0.6\text{sin}\big{(}0.02(t-200)\big{)}+0.4,&t\geq 200.\end{cases} \]  
Numerical simulations are performed with a sampling frequency of 0.04 s and compared under three different control methods. 1. Event-triggered networked predictive fault-tolerant control (ENPFTC): When agent 1 encounters an actuator fault at 8 s, after compensation by the controller, the system output quickly returns to the vicinity of the reference value as shown in Figure 3, and the tracking error converges to near zero, while the maximum tracking error is less than 0.5 as shown in Figure 4, indicating that the designed fault-tolerant control method can actively compensate for actuator faults. When the system is stabilized, the event trigger effectively reduces the amount of data transmission in the feedback channel of the agent, the number of event triggers are 478/600, 483/600, 461/600 and 469/600, the statistics of event trigger counts show that the event trigger can reduce the data transmission volume by about 21%, and the event trigger record is shown in Figure 5, where \"1(0)\" means that the event trigger is (not) triggered. In addition, we updated the actuator fault \(f_{1}(t)\) to \(1.2\text{sin}(0.02(t-200))+0.4\) when \(t\geq 200\), and repeated the simulation. The output result and tracking errors of ENPFTC are shown in Figure 6 and Figure 7, respectively. 2.