Search Results (4)

The increasing reliance on and remote accessibility of automated industrial systems have shifted SCADA networks from being strictly isolated to becoming highly interconnected systems. The growing interconnectivity among systems enhances operational efficiency and also increases network security threats, especially attacks from industrial viruses. This paper focuses on the stability analysis and optimal control analysis for a fractional-order industrial virus-propagation model based on a SCADA system. Firstly, we prove the existence, uniqueness, non-negativity and boundedness of the solutions for the proposed model. Secondly, the basic reproduction number ${\mathcal{R}}_0^{\alpha }$ is determined, which suggests the conditions for ensuring the persistence and elimination of the virus. Moreover, we investigate the local and global asymptotic stability of the derived virus-free and virus-present equilibrium points. As is known to all, there is no unified method to establish a Lyapunov function. In this paper, by constructing an appropriate Lyapunov function and applying the method of undetermined coefficients, we prove the global asymptotic stability for all possible equilibrium points. Thirdly, we formulate our system as an optimal control problem by introducing appropriate control variables and derive the corresponding optimality conditions. Lastly, a set of numerical simulations are conducted to validate the findings, followed by a summary of the overall study. Full article

In the information age, frequent information exchange has provided a breeding ground for the spread of computer viruses. The significant losses caused by computer virus attacks have long rung the alarm for information security. From academia to businesses, and even to government, everyone remains highly vigilant about information security. Researchers have put forward various approaches to combat computer viruses, involving innovative efforts in both the hardware and software aspects, as well as theoretical innovation and practical exploration. This article is dedicated to theoretical exploration, specifically investigating the stability of a computer virus model, known as SLBRS, from the perspective of optimal control. Firstly, a control system is introduced with the aim of minimizing the costs related to network detoxification and diminishing the percentage of computers impacted by the virus. Secondly, we employ the Pontryagin maximum principle to analyze the optimality of a control strategy for the proposed system. Thirdly, we validate the effectiveness of our theoretical analysis through numerical simulation. In conclusion, both theoretical analysis and numerical simulation reveal that the utilization of optimal control analysis to stabilize the SLBRS has been demonstrated to be advantageous in restoring contaminated computer network environments. Full article

Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viruses, including antivirus software and internet firewalls. In this paper, we focus on investigating computer virus transmission from the perspective of mathematical modeling. Our main contributions in this paper are threefold: (1) we improve the classical SLBRS model by incorporating cure rates, effectively capturing the dynamics of computer network maintenance; (2) we introduce an optimal control system within the SLBRS framework, with the dual objectives of minimizing network detoxification costs and reducing the proportion of broken-out nodes; and (3) by employing Pontryagin’s Maximum Principle, we establish the existence and uniqueness of an optimal control strategy for the proposed control system. Furthermore, we perform numerical simulations to demonstrate the effectiveness of our theoretical analyses. Full article

In the case of low frequencies (e.g., P-band) radar observations, the Gaussian Vertical Backscatter (GVB) model, a model that takes into account the vertical heterogeneity of the wave-canopy interactions, can describe the forest vertical backscatter profile (VBP) more accurately. However, the GVB model is highly complex, seriously reducing the inversion efficiency because of a number of variables. Given that concern, this paper proposes a constrained Gaussian Vertical Backscatter (CGVB) model to reduce the complexity of the GVB model by establishing a constraint relationship between forest height and the backscattering vertical fluctuation (BVF) of the GVB model. The CGVB model takes into account the influence of incidence angle on scattering mechanisms. The BVF of VBP described by the CGVB model is expressed with forest height and a polynomial function of incidence angle. In order to build the CGVB model, this paper proposes the supervised learning based on RANSAC (SLBR). The proposed SLBR method used forest height as a prior knowledge to determine the function of incidence angle in the CGVB model. In this process, the Random Sample Consensus (RANSAC) method is applied to perform function fitting. Before building the CGVB model, iterative weighted complex least squares (IWCLS) is employed to extract the required volume coherence. Based on the CGVB model, forest height estimation was obtained by nonlinear least squares optimization. E-SAR P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) data acquired during the BIOSAR 2008 campaign was used to test the performance of the proposed CGVB model. It can be observed that, compared with Random Volume over Ground (RVoG) model, the proposed CGVB model improves the estimation accuracy of the areas with incidence angle less than $0.8$ rad and less than $0.6$ rad by $28.57\%$ and $40.35\%$ , respectively. Full article