# Change Control Design in Product Supply Chain System Based on Radial Basis Function Neural Network
###### Abstract
Nevertheless, sliding mode control experiences jitter vibration and has high requirements on the dynamic response of the system, which may increase control complexity and implementation difficulty in practical applications. A study [10] introduced a multi-intelligent reinforcement learning approach based on a Partially Observable Markov Decision Process (POMDP) model for solving the inventory management problem in a multi-node, multi-material supply chain model in civil aircraft manufacturing. The method has strict requirements for the accurate modeling of the environment, is computationally complex, and may suffer from inefficiencies in information sharing and coordination. A study [11] tackled the problem of uncertain demand fluctuations and unforeseen events in product and supply chain systems by designing TS fuzzy rules to coordinate different subsystems that describe the corresponding production and inventory processes. It also suggested designing change control to handle systems subject to blockages or disruptions. However, the construction and optimization process of TS fuzzy rules is complicated, and its control accuracy and adaptability may be limited when facing highly nonlinear and time-varying parameters. To address these challenges, the literature  
Figure 1: Schematic diagram of ideal inventory chain. proposes a linear quadratic regulator (LQR) control [12] method, which does not require complex parameter tuning, is able to monitor the inventory status and demand changes in real time, and quickly adjusts the control strategy in order to avoid the loss of control or collapse of the supply chain. Compared with other methods, the LQR method has strong robustness and can effectively deal with disturbances and uncertainties in the system and can avoid the jitter problem. A study [13] further proposed an online LQR dynamic control method with time-varying eigenfunctions and perturbations, which can optimize the adaptability of complex supply chains. The lateral feedforward control method combined with predictive LQR proposed in the literature [14] can better adapt to the lateral tracking problem of intelligent vehicles under complex working conditions, demonstrating the wide applicability of the LQR control method in different application scenarios. Studies in the literature [15] show that LQR controllers excel in terms of performance as well as robustness, are able to reduce the deviation of the state trajectory with minimal control force, and reduce the impact of disturbances on the system. This makes LQR valuable for a wide range of applications in real-world projects such as autopilot [16; 17], satellite formation [18; 19], and high-altitude ballooning [20], especially in dealing with disturbances such as uncertain demand fluctuations in and external attacks to the supply chain, which can effectively maintain the stability of a system. In addition to the complex uncertainties both inside and outside the system, the modern product supply chain has also benefitted from the development of big data and artificial intelligence technologies. It is gradually transforming in the direction of digitization and intelligence [21], evolving into an information-physical system (CPS) driven by digital technology, with the collaborative management of product production, transportation, and sales [22]. Product supply chain systems, such as typical CPSs, have a high dependence on transmission and collaborative operation [23], making them easy targets for cyber-attacks [24]. Attackers can paralyze a system or tamper with the data through cyber-intrusion [25], such as malware attacks [26], false data injection attacks [27], data leakage, and denial-of-service attacks [28; 29] (DoS). A DoS attack refers to an attacker's exploitation of a system vulnerability to prevent legitimate systems from accessing services or system resources in a timely manner through malicious actions [30].