Fractional Optimal Control for Malware Propagation in Internet of Underwater Things

The Internet of Underwater Things (IoUT) relies on wireless communication devices that are arranged in an open underwater environment and can interact with other devices through acoustic communication technology. However, due to their limited resources and open underwater environment, IoUT has been suffering from a high risk of malware attacks. As the two main parts of IoUT, autonomous underwater vehicles (AUVs) and underwater wireless rechargeable sensor networks (UWRSNs) are more favored by attackers and can be directly attacked by malware, which can lead to the cross-propagation of malware when AUVs and UWRSNs exchange information. To mitigate that threat, there is an urgent need to study the propagation patterns of malware and control their spread. Therefore, we establish a mathematical model based on the fractional-order theoretical framework to investigate the malware propagation patterns in two coupled networks (UWRSNs and AUVs). Then, we combine immune, charging, and quarantine delays in control and derive the optimal control strategies based on optimal control theory. Moreover, to improve the generality of control, we propose a machine learning (ML) controller that combines ML [e.g., deep neural network (DNN) and random forest (RF)] with control theory. Ultimately, our simulation experiments show that the proposed optimal control strategy is more effective in inhibiting the spread of malware while obtaining the minimum control cost under different fractional-order scenes. At the same time, the ML-based control results are close to the optimal control.