The rapid proliferation of Internet of Vehicles (IoV) technology has significantly enhanced traffic efficiency and driving safety, yet it has also introduced severe security challenges due to malware and cyberattacks. This paper proposes a novel Fractional-Order Attack-Defense Game model (FADG-IoV) to address dynamic malware propagation in IoV environments. By integrating fractional-order dynamics, the model accounts for communication delays, traffic density heterogeneity, and channel fading, capturing memory-dependent behaviors inherent in IoV systems. We introduce the Fractional-Order Attack-Defense Game Sparse Attention Multi-Agent Soft Actor-Critic (FADG-SMASAC) algorithm, a model-free reinforcement learning approach that leverages sparse attention mechanisms to achieve adaptive and robust control without requiring a known system model. Through multi-baseline experiments, we validate the FADG-IoV model and FADG-SMASAC algorithm, demonstrating superior convergence, scalability, and robustness compared to existing methods. Our findings highlight the effectiveness of fractional-order game-theoretic strategies in enhancing IoV security against dynamic malware threats, paving the way for future research in adaptive defense mechanisms.

Malware propagation in Internet of Underwater Things (IoUT) can disrupt stable communications among wireless devices. Timely control over its spread is beneficial for the stable operation of IoUT. Notably, the instability of the underwater environment causes the propagation effects of malware to vary continuously. Traditional control methods cannot quickly adapt to these abrupt changes. In recent years, the rapid development of reinforcement learning (RL) has significantly advanced control schemes. However, previous RL methods relied on long-term interactions to obtain a large amount of interaction data in order to form effective strategy. Given the particularity of underwater communication media, data collection for RL in IoUT is challenging. Therefore, improving sample efficiency has become a critical issue that current RL methods need to address urgently. The algorithm of Attention-Model-Based Multiagent Policy Optimization (AMBMPO) is proposed to achieve efficient use of data samples in this study. First, the algorithm employs an explicit prediction model to reduce the dependence on precise model. Secondly, an attention mechanism network is designed to capture high-dimensional state sequences, thereby reducing the compound errors during policy training. Finally, the proposed method is validated for optimal control problems and compared with verified benchmarks. The experimental results show that, compared with existing advanced RL algorithms, AMBMPO demonstrates significant advantages in sample efficiency and stability. This work effectively controls the spread of malware in underwater systems through an interactive evolution based approach. It provides a new implementation approach for ensuring the safety of underwater systems in deep-sea exploration and environmental monitoring applications.

To address the dynamic control challenges of malware propagation in smart agricultural UAV-WSN (Unmanned Aerial Vehicle-Wireless Sensor Network) systems, this paper proposes a novel hybrid control modeling framework based on fractional-order calculus. A 14-dimensional dual-layer SEIQR-SEIQRL fractional-order propagation model with time-delay effects is established to characterize cross-layer infection mechanisms between UAVs and sensor nodes, as well as system memory properties. By innovatively integrating direct treatment and dynamic quarantine strategies, and further incorporating node energy constraints, this study formulates an optimal control problem. To overcome the dependency of traditional numerical solutions on system models, a reinforcement learning (RL)-based decision framework is designed, which integrates the Proximal Policy Optimization (PPO), Soft Actor-Critic (SAC), Twin Delayed Deep Deterministic policy gradient (TD3) and Multi-Agent Soft Actor-Critic (MASAC) algorithms. Experimental results validate the memory advantages of the proposed fractional-order theory, the effectiveness of hybrid control strategies, and the adaptability of RL-based solvers. This study provides a dynamically defensive architecture with memory-aware capabilities, offering both theoretical innovation and engineering applicability for IoT security in smart agriculture, thereby supporting reliable data acquisition in sustainable precision agriculture.

Autonomous Underwater Vehicle (AUV)-assisted Underwater Wireless Sensor Networks (UWSNs) offer transformative potential for data collection, disaster prediction and environmental monitoring. However, these networks remain critically vulnerable to malware attacks due to inherent communication challenges and limited energy resources. To rigorously capture the spatiotemporal dynamics of malware propagation, this paper introduces a novel two-layer heterogeneous model rooted in Partial Differential Equations (PDEs). To suppress malware propagation under limited bandwidth, this paper proposes a spatiotemporal optimal control strategy integrating saturation functions. The existence of the optimal pair is demonstrated by the minimizing sequence method, and the first-order necessary condition for spatiotemporal control is derived based on convex perturbation methods. Further, extensive numerical experiments validate the effectiveness of the proposed two-layer heterogeneous model and spatiotemporal control strategy. Finally, the applications of the proposed model and control strategy in real-world scenarios are discussed.

Internet of Vehicles (IoV) is gradually becoming popular, but it also brings more opportunities for malware intrusion. The intrusion of malware into IoV will cause a series of security issues and increase the incidence of road accidents. Therefore, the suppressing measures to combat the spread of malware in IoV will be fundamental and urgent. To address this critical issue, this paper proposes a fractional-order IoV (FIOV) to investigate malware propagation patterns in Road Side Unit (RSU) and Vehicles. To accurately reflect the actual spread of malware, the traffic density, the channel fading and the actual connectivity are considered in mathematical model. Then, the model-based optimal treatment and quarantine control strategy is derived by optimal control theory. Additionally, a novel model-free FIOV multi-agent soft actor-critic (FIOV-MASAC) approach is first proposed to suppress the malware propagation in IoV. Simulation experiments demonstrate that the proposed FIOV-MASAC approach exhibits better learning ability compared to other reinforcement learning (RL) algorithms.Note to Practitioners—Frequent attacks by malware on IoV are recognized as being challenging to prevent, with these attacks posing threats to data security and potentially resulting in traffic accidents and vehicle malfunctions. In response, a novel mathematical model has been introduced within this study to better predict the propagation trends of malware in IoV, effectively managing its spread within the vehicular network systems. While RL methods have been extensively utilized in the domain of control systems, it is noted that current RL methods depend on rich experience pools, rendering them inapplicable to more complex systems without adaptation. To address this, an effective and pragmatic RL algorithm has been devised in this study. This algorithm, devoid of the requirement for complex model establishment, is capable of intelligently learning and adjusting to the sophisticated environment of IoV, thereby effectively countering the propagation of malware. It should be highlighted that the RL method proposed herein is applicable to the majority of epidemic systems, enabling the achievement of stable control while substantially minimizing control expenditures. The integration of this method is anticipated to augment the security and robustness of IoV in the face of malware attacks.

Toward exploring the positive impact of media debunking and random blocking on the spread of rumors, we discuss a stochastic hybrid control strategy that combines an individual and media debunking method, a continuous stochastic blocking method, and an impulse interruption method. Using stochastic analysis, the almost sure exponential stability of the controlled system is analyzed, along with the expression of control intensities. To balance rumor suppression, minimize control costs, and enhance the generality of control, a data-driven machine learning (ML) approach is developed to provide suboptimal control solutions. Numerical simulations based on two real-case datasets are carried out to validate the theoretical results and evaluate the potential impact of the model-based, data-driven stochastic hybrid control strategy.

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.

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.

Unmanned aerial vehicle (UAV) and wireless sensor network (WSN) system widely used in emergency sites monitoring, disaster relief and data collection, is vulnerable to malware attack. In this article, we establish a novel epidemic model to accurately describe the characteristics of malware cross-propagation and stochastic disturbances between UAV and WSN. To control their spread, the hybrid charging and patching strategies are optimized by the proposed stochastic hybrid optimal control (OC) method while minimizing control costs. An effective stacking ensemble learning control (SELC) approach is developed to obtain a sub-OC strategy. Extensive comparison and simulations are shown to validate the effectiveness of the proposed stochastic hybrid OC method and SELC method.

This study examines the intermittent control of a rumor propagation system with anti-rumor mechanism. The interaction with the anti-rumor mechanism is investigated, including the existence and stability of two boundary equilibriums, the condition of bistability behavior. Threshold parameters are identified which determine the global exponential stability of the rumor-free equilibrium. To combat rumor spreading, we design deterministic and stochastic control strategies with aperiodically intermittent control time. The expressions of the minimum control intensities are obtained, which are related to the control ratio and system parameters. Numerical examples are carried out to verify the validity of the theoretical results and evaluate the potential roles of the intermittent control strategies.

In this article, a wireless multirelay network in which the relays are energy constrained is studied. Especially, in order to consume the harvested energy efficiently at the relays so as to improve the network throughput, a new hybrid relaying protocol is first proposed. In the proposed protocol, each relay can flexibly switch its operation among energy harvesting (EH), information receiving (IR), active information transmission (IT), and two passive backscatter communication (BC) modes according to the channel states as well as its data buffer states and energy states in each transmission block, by which the harvested energy can be efficiently utilized and superior throughput performance can be achieved. However, under the hybrid relaying protocol, it is challenging to achieve a strategy to optimally determine the operation mode for each relay, and the energy and information scheduling at the relays that operate in the IR, IT, and BC modes. To address this issue, the involved optimization problem is formulated as a stochastic optimization problem, which cannot be tackled directly. To make it tractable, the stochastic optimization problem is transformed into a Markov decision process (MDP) with finite state and action spaces. By solving the MDP via a dynamic programming (DP) algorithm, the optimal strategy for the multirelay network is achieved. Furthermore, to reduce the computational complexity in the DP algorithm, an efficient algorithm with low complexity is developed by using a Lyapunov optimization framework. Numerical simulations show that our proposed hybrid relaying strategy can achieve superior throughput performance in wireless multirelay networks.

This article studies a network where a transmitter communicates with a receiver by hybrid communications that consist of passive information transmission (IT) via backscatter communication (BC) and active IT via wireless-powered communication (WPC). Because the circuit energy consumption in the passive IT of BC is much lower than that in the active IT of WPC, BC usually achieves a higher data transmission rate than WPC. Thus, it was suggested in the literature that the network throughput performance could not be improved by hybrid communications. However, our work in this article demonstrates that the throughput can be enhanced by a newly designed hybrid communication strategy. To demonstrate this, we develop a novel protocol that enables the transmitter to adaptively switch its operation between BC, active IT, and energy harvesting in one time block while scheduling energy consumption flexibly among multiple time blocks. Under the developed protocol, we formulate an optimization problem to jointly optimize the operation mode and resource allocation at the transmitter. The formulated problem is difficult to solve because the energy scheduling at the transmitter is coupled across multiple time blocks, and noncausal channel state information (CSI) is required. To address this problem, we first solve a simplified optimization problem via dynamic programming (DP) and a layered optimization method by assuming that the noncausal CSI is known. Then, we employ an approximate DP approach to solve the original problem with causal CSI. Finally, we verify by simulations that the proposed scheme can achieve superior throughput performance.

Abstract The problem of target location estimation in a wireless sensor network is considered, where due to the bandwidth and power constraints, each sensor only transmits one‐bit information to its fusion center. To improve the performance of estimation, a position‐based adaptive quantization scheme for target location estimation in wireless sensor networks is proposed to make a good choice of quantizer' thresholds. By the proposed scheme, each sensor node dynamically adjusts its quantization threshold according to a kind of position‐based information sequences and then sends its one‐bit quantized version of the original observation to a fusion center. The signal intensity received at local sensors is modeled as an isotropic signal intensity attenuation model. The position‐based maximum likelihood estimator as well as its corresponding position‐based Cramér–Rao lower bound are derived. Numerical results show that the position‐based maximum likelihood estimator is more accurate than the classical fixed‐quantization maximum likelihood estimator and the position‐based Cramér–Rao lower bound is less than its fixed‐quantization Cramér‐Rao lower bound. Copyright © 2015 John Wiley & Sons, Ltd.

The problem of distributed estimation of an unknown noise-corrupted parameter in wireless sensor networks, with a fusion centre, is considered. Convolutional coding and rate-compatible punctured convolutional coding are used to protect the transmission of sensor observations and to reduce the impact of noise channels. Two novel kinds of power scheduling based on different encoding methods are derived for minimising the total power consumption. The formulas of the proposed power scheduling suggest that local sensors with poor observation qualities should decrease their quantisation levels. The levels should also be related to coding methods, channel qualities, a given mean squared error (MSE) and local signal-to-noise ratios. Finally, simulation results show that not only these two schemes are energy-efficient but also they can achieve comparable performance of a given MSE.