# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
## 4 Simulation Analysis  
In order to verify the correctness and effectiveness of the proposed method, we used the Matlab2019a simulation platform, and the effectiveness of the proposed method was verified through simulation examples. During semiconductor production and manufacturing, semiconductor product supply chain systems often exhibit significant time-varying characteristics due to the operational volatility of production equipment and natural wear during inventory storage. At the same time, market demand is often cyclical, creating even greater challenges for inventory man agement and production control. As shown in Figure 4, by combining the operational data from semiconductor companies [33] and analyzing the historical data from semiconductor supply chain factories, we identified patterns and modeled the production pass rate and inventory loss rate to more accurately characterize their dynamics:  
\[A= \begin{bmatrix}-0.5&0\\ 0&-0.15\end{bmatrix} ,\]  
\[B= \begin{bmatrix}1&0\\ -1&1\end{bmatrix} ,D= \begin{bmatrix}0.1\\ 1\end{bmatrix} \]  
In actual production, the factory's initial inventory is represented by a vector \(x(0)=[5,5]^{T}\), which reflects the initial quantities of two inventory items. To satisfy market demand and optimize operational efficiency, the factory aims to gradually deplete its inventory using a dynamic control strategy, ultimately bringing the inventory to zero. Since market demand is often unstable and fluctuates periodically, external demand is modeled as a periodic signal to capture the cyclical nature of these fluctuations. During the process of producing a product, external disturbances can alter the supply chain structure. In this paper, we evaluate the impact of the RBFNN feedforward control on the controller's performance. Figure 5 shows the effect of pure LQR control on the system without the addition of RBFNN feedforward control. It is evident that the system's inventory fluctuates in response to disturbances from uncertain user demand. The magnitude of these fluctuations is proportional to the size of the disturbance. Figure 4: Basic steps in semiconductor manufacturing. Figure 5: Trajectory of inventory in LQR system without RBFNN. The addition of RBFNN predictive feedforward control and its effect on the system are shown in Figure 6. It can be seen that the product inventory fluctuations are significantly reduced to negligible levels due to the prediction of uncertain user demand disturbances by the RBFNN, which demonstrates a significant improvement in the control performance achieved by using RBFNN to approximate the unknown disturbances. It is worth mentioning that the transient inventory phase in Figure 6 shows small oscillations before stabilizing, as the RBFNN has not yet accurately approximated the unknown disturbance during the initial period after system initialization. Figures 7 and 8 illustrate the impact of the RBFNN on approximating unknown disturbances. The solid line represents the actual disturbance, while the dashed line shows the RBFNN's estimation of the disturbance. During the first 3 s, the RBFNN weights have not yet reached optimal values, leading to significant bias in the disturbance prediction. This results in suboptimal performance during the inventory's transient phase, as shown in Figure 6. However, with continuous operation of the control system, the RBFNN learns more effectively and approximates unknown disturbances with increasing accuracy over time. As a result, if the system's inventory undergoes significant changes, the inventory variables can closely converge to the optimal control effect. Figure 9 displays the production control signals of controller (17) for the two product plants. The solid line represents the control signal for the plant providing the raw materials, while the dashed line represents the control signal for the plant responsible for the end product. It is evident that the control signals exhibit periodic changes in response to disturbances, effectively suppressing their impact.