Hybrid control for malware propagation in rechargeable WUSN and WASN: From knowledge-driven to data-driven

Rechargeable wireless underground sensor network (WUSN) and wireless aboveground sensor network (WASN) provide information transfer services for acquiring aboveground and underground interactive data. However, due to the limited energy, computation, storage and the open environment, sensors are often attacked by malware and their power supply is usually exhausted earlier. In this paper, a novel model with two-layer structure is proposed to depict the dynamic process of malware cross-propagation between rechargeable WUSN and WASN, which takes into account both infection delay and low energy. To further overcome the problem of malware propagation and battery depletion, three hybrid control strategies including continuous recovery, impulse quarantine with isolation delay and pulse charging are proposed. Then, to suppress malware propagation under the minimum cost, the necessary conditions for the model-based knowledge-driven optimal control (MKOC) are solved by the variational method. Moreover, to improve the practical utilization of MKOC, the novel neural network-based data-driven control (NNDC) is proposed based on feedforward neural network (FNN), gated recurrent unit (GRU) and long short-term memory (LSTM). Finally, through numerical simulations, the effects of various quarantine parameters on the total costs and the influence of each control strategy on state curves and control curves are revealed, respectively; meanwhile, the effectiveness of MKOC and NNDC is evaluated by comparing their control costs. •A malware propagation control mathematical model for rechargeable WUSN and WASN is proposed.•The optimality system for the optimal control problem is derived.•Neural network-based data-driven control is obtained to improve control performance.