# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
## 4 Simulation Analysis
Figure 6: Inventory control trajectory for supply chain system after adding RBFNN. Figure 8: The effect of the RBF network in approximating an unknown disturbance \(f_{2}\). Figure 7: The effect of the RBF network in approximating the unknown disturbance \(f_{1}\). In the above case, the supply chain system is not attacked from the outside. When the supply chain suffers a DoS attack during operation, suppose the active periods of the DoS attack occur on the fifteenth and twentieth days. At this point, the RBFNN can be used to predict the system inventory and replace the disturbed inventory values that were affected by an attack with the predicted values. For parameter selection, we randomly selected data points as the center values after the system stabilized. The width of the neural network was chosen using the cross-validation method, where the model's performance with different widths was evaluated, and the optimal width was selected. For selecting the number of neurons in the hidden layer, we used a step-by-step verification method, starting with a small number of neurons, gradually increasing the number of neurons, and observing the changes in error until we found the optimal number of neurons with minimal error and moderate complexity. By taking these steps, we ensured that the inventory data were tracked accurately. As shown in Figure 10, in the absence of external control, systematic inventory control can be greatly disturbed or even collapse. However, under the same control conditions, after effective control by the controller, the system can quickly return to a stable state, with the inventory level approaching the ideal level after the controller adjusts it. Figure 11 shows the changes in the controller's performance after the attack. Clearly, at the moment of the attack, the controller exhibits performance fluctuations, but it reacts promptly and adjusts to achieve optimal control. The results demonstrate that the proposed composite controller exhibits strong asymptotic stability when the system is subjected to unknown disturbances or attacks. Figure 9: Production control signals for two product plants. Based on these results, we compared the effects of the RBFNN and Kalman filtering on system performance following a DoS attack. As shown in Figure 10b, the RBFNN effectively predicts the inventory changes and makes timely adjustments to the system, ensuring its stability. In contrast, Figure 12 demonstrates that Kalman filtering exhibits inferior prediction performance, with slow recovery and significant fluctuations after the DoS attack, failing to stabilize the inventory level effectively. Therefore, the RBFNN clearly outperforms Kalman filtering in handling DoS attacks, providing better system control and prediction performance. To validate the effectiveness of the control method, we also conducted a comparative experiment. Following the approach outlined in the work by [PERSON] et al. [8], we employed the traditional PID control method. Figure 11: Production control signals for two product plants. Figure 10: Comparison of pre\(-\)control (**a**) and post\(-\)control (**b**) system inventory tracking changes after a DoS attack. Although PID control can achieve some stability and responsiveness, it struggles to quickly suppress the influence of the bullwhip effect due to its poor robustness to perturbations and system parameter changes as well as its low control accuracy. This hysteresis can cause the system state to deviate from the target for extended periods, especially under complex dynamic changes, which are prone to large tracking errors and delays. The hysteresis and limited inhibitory ability of PID control can further aggravate inventory fluctuations, leading to an unbalanced supply of raw materials or semi-finished products, thus disrupting production rhythm as well as negatively impacting system stability and product quality. Figures 13 and 14 show the dynamics of the inventory and controller under the effect of PID control, respectively.