# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
###### Abstract
In product supply chain systems, this can manifest as a delay or loss of inventory status information, which can have a serious impact on critical and real-time services [31]. Scholars both domestically and internationally have made significant progress in mitigating the effects of DoS attacks on control systems. A study [32] proposed a dynamic memory event-triggering mechanism that includes memory items and suggested combining a switching fuzzy model with a multi-Lyapunov function strategy to counter network attacks. A study [33] enhanced the robustness and resilience of supply chain systems against complex nonlinear disturbances and cyber-attacks by combining RBF neural networks with improved sliding mode control. The literature [34] proposes a secondary control framework for inverter-based distributed generation (DG) systems for effectively coping with the problem of islanded microgrids subject to DoS attacks. The literature [35] proposes a finite interval search method of obtaining the optimal starting moment of a DoS attack and compensating for it, addressing the problem of DoS attacks on LQR control channels. Researchers [36] proposed an artificial neural network-based architecture for detecting and isolating DoS attacks with CPS integrity. Authors [37] tackled the problem of Hoo state estimation for discrete-time amnestic neural networks with time-varying delays and proposed a state estimation method that ensures the error system's dynamics are exponentially mean-square-stabilized while satisfying a prescribed level of Hoo interference decay. In distributed cyber-physical systems, DoS attacks can disrupt communication links and significantly increase co-tracking errors, which in turn affect the stability and coordination of the system. The neural network approach can adaptively identify attack patterns in network traffic and effectively reduce the damage caused by DoS attacks on the system through intelligent control and optimization strategies, thus maintaining the security and operability of the system. The literature [38] proposes a convolutional neural network (CNN)-based intrusion detection method to address variable network attacks to achieve efficient defense. Therefore, in view of the powerful prediction capability of neural networks, this paper further proposes a predictive control method based on a Radial Basis Function Neural Network [39] (RBFNN). Compared with traditional prediction methods such as Kalman filtering, RBFNN has significant advantages in dealing with DoS attacks. Although Kalman filtering is excellent in dealing with linear systems and Gaussian noise, its performance degrades significantly in nonlinear systems or non-Gaussian noise environments; especially in cases with data loss or delay due to DoS attacks, the prediction accuracy and robustness of Kalman filtering are greatly affected. Therefore, RBFNN prediction can improve the robustness and stability of a system and ensure continuous and stable operation in the face of data loss or delay caused by DoS attacks. In this paper, to investigate the change control problem in product supply chain systems under cyber-attacks, an optimal linear quadratic regulator control strategy for product supply chains based on the RBFNN is proposed. In order to cope with time-varying disturbances due to parameter changes in supply chain systems caused by uncertain external user demand or environmental factors, adaptive RBF neural networks (RBFNNs) are employed for compensatory control to improve system performance. When the system is subjected to a DoS attack, the RBFNN can quickly predict inventory changes and ensure the continuous and stable operation of the system through predictive control. Compared with the traditional composite control method, the method proposed in this paper reduces the dependence on the accuracy of the model through the adaptive control of the neural network, which effectively reduces the computational cost.