# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
###### Abstract  
Product supply chain systems are structurally complex infophysical systems that contain numerous unmodeled dynamics and uncertainties. Drastic fluctuations in user demand and sudden unexpected events--such as epidemics, trade wars, or cyber-attacks--can lead to changes in system structure or parameters or even destabilize the system. Designing changes within the product supply chain is an important strategy to meet user demand and maintain stable system operation. In this paper, we explore the use of artificial intelligence (AI) to enhance the analysis and control of complex product supply chain systems. We design a radial basis function neural network (RBFNN) to address Denial of Service (DoS) attacks. This RBFNN is designed to predict trends in inventory changes following a system attack and to develop optimal control strategies accordingly. First, we construct a mathematical model of the product supply chain system. Second, we leverage the predictive capability of the RBFNN to handle the effects of system changes and cyber-attacks through feed-forward compensatory control. A Linear Quadratic Regulator (LQR) is then designed under the nominal system. Finally, we verify the effectiveness of the proposed method through simulation experiments. product and supply chain system; cyber-attack; linear quadratic regulator controller; radial basis function neural networks +
Footnote †: journal: Applied sciences  
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Modern product supply chain systems are characterized by a large number of unmodeled dynamics and uncertainties, dramatic demand fluctuations and unexpected network events, making them highly susceptible to changes in system structural parameters. Inaccurate production design can also lead to problems such as inventory backlog and low resource utilization [4]. Therefore, in-depth research on inventory management in product supply chain systems is particularly important [5]. However, most previous studies have focused on areas such as product supply chain freight planning, supplier selection, and supply chain energy consumption, with little attention paid to the inventory control challenges faced by manufacturers. In fact, the inventory in a product supply chain system is affected by a variety of factors, among which market demand is the key force driving the operation of the system. When market demand changes, it manifests as uncertainty in user-side demand, which propagates and amplifies throughout the supply chain, ultimately triggering the bullwhip effect [6]. This leads to overproduction, cost increases, and other problems. Furthermore, when the product supply chain system is subjected to environmental changes or disturbances [7], system parameters may change, leading to decreased control performance, which further affects the stability of the system. Due to dramatic demand fluctuations, network events, and environmental changes triggered by system parameter changes, the modern product supply chain system faces uncertainty and the bullwhip effect, which impact inventory control and system stability. Researchers [8] designed control loops based on PID controller algorithms for the dynamic adjustment of the components of a continuous review system (Q system) to optimize inventory management. Although PID control performs well in simple linear systems, its ability to handle nonlinearities, time-varying parameters, and external disturbances is limited, especially in complex supply chain environments, where it is difficult to meet the need for high accuracy and robustness. A study [9] proposed a nonlinear supply chain system production change optimization model based on improved adaptive sliding mode control. This model addresses the issue of upstream manufacturers being unable to accurately formulate production plans after a change in the link of a nonlinear supply chain system due to unexpected events.