Spatiotemporal Control Optimization of Malware Propagation in Internet of Underwater Things

Internet of Underwater Things (IoUT), widely utilized in data collection, ocean exploration and disaster prevention, are prone to malware attacks. To accurately describe the spatiotemporal dynamics of malware propagation in IoUT, a new Reaction-Diffusion Sleep Control Model (RDSCM) based on Partial Differential Equations (PDEs) is established in this paper. To target heavily infected regions and optimize control costs, a spatiotemporal hybrid optimal control strategy is implemented. First, based on the formulation of the spatiotemporal optimal control problem, the existence, uniqueness, and some estimates of the strong solution of the controlled system are obtained using the truncation method and semigroup theory. Then, the existence of the optimal pair is verified through the minimization sequence technique. Subsequently, the first-order necessary optimality condition for the optimal control problem of PDEs is derived by proving the differentiability of the control-to-state mapping. To validate the effectiveness of the proposed model and control methodology, three comparative experimental studies are conducted. Finally, some discussions are provided on the extension and application of the proposed method.