A new Takagi-Sugeno fuzzy system approach for fuzzy state feedback controller design and its application to malware propagation on heterogeneous complex network
DOI:
https://doi.org/10.54654/isj.v3i20.988Keywords:
Fractional network-based model, SCIRS malware propagation model, interconnected Takagi-Sugeno fuzzy system, fuzzy state feedback controlTóm tắt
Abstract— Nowadays, digital transformation has brought many great changes and is becoming an essential part of real life, however, it also goes along with a considerable likelihood of being targeted in cyberattack. Indeed, the more businesses embrace digital transformation or use online services, the more opportunities hackers have to expand their cyberattacks. Hence, there is an essential need on analyzing and predicting of cyberattack on network systems. For this aim, we propose to study a controlled fractional network-based SCIRS (Susceptible - Carrier - Infectious - Recovered - Susceptible) malware propagation model and its stabilization problem based on fractional interconnected Takagi-Sugeno fuzzy system. A fuzzy state feedback controller is proposed to asymptotically stabilize the unstable malware-free equilibrium of the proposed malware propagation model and then, we establish sufficient conditions in terms of linear matrix inequalities. The effectiveness of proposed approach is illustrated by a case study of SCIRS malware propagation model on heterogeneous complex network.
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References
Y. Chen, F. Liu, Q. Yu & T. Li, “Review of fractional epidemic models”, Appl. Math. Model., 97 (2021), pp. 281-307.
K. Diethelm, “The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type”, Lecture Notes in Mathematics, Vol. 2004, Springer-Verlag, Berlin, 2010.
J.D. Hernández Guillén and A. Martín del Rey, “Modeling malware propagation using a carrier compartment”, Commun. Nonlinear Sci. Numer. Simulat., 56 (2018), pp. 217–226.
J.D. Hernández Guillén and A. Martín del Rey, “A mathematical model for malware spread on WSNs with population dynamics”, Physica A, 545 (2020), pp. 123609.
S. Hosseini and A. Zandvakili, “The SEIRS-C model of information diffusion based on rumour spreading with fuzzy logic in social networks”, Inter. J. Comput. Math., 99 (9) (2022), pp. 1918-1940.
S. Huang, F. Chen and L. Chen, “Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination”, Commun. Nonlinear Sci. Numer. Simulat., 43 (2017), pp. 296-310.
J. Huo and H. Zhao, “Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks”, Phys. A, 448 (2016), pp. 41-56.
W.O. Kermack and A.G. McKendrick, “A contribution to the mathematical theory of epidemics”, Proc. Roy. Soc. London, 115 (1927), pp. 700-721.
H.J. Lee, “Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: Positive Takagi–Sugeno model approach”, Biomed. Signal Process. Control, 72 (2022), Part A, pp. 103273.
Z. Lendek, T. Guerra, R. Babuska and B. De Schutter, “Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models”, in Studies in Fuzziness and Soft Computing, Springer, vol. 262, 2010.
Y. Li and J. Li, “Stability analysis of fractional order systems based on T-S fuzzy model with the fractional order ”, Nonlinear Dyn., 78 (2014), pp 2909–2919.
K. Li, G. Zhu, Z. Ma and L. Chen, “Dynamic stability of an SIQS epidemic network and its optimal control”, Commun. Nonlinear Sci. Numer. Simulat., 66 (2019), pp. 84-95.
W.W. Lin, W.J. Wang and S.H. Yang, “A novel stabilization criterion for large-scale T-S fuzzy systems”, IEEE Trans. Syst. Man Cybern. B. Cybern., 37 (4) (2007), pp. 1074-9.
M.A. Duarte-Mermoud, N. Aguila-Camacho, J.A. Gallegos and R. Castro-Linares, “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems”, Commun. Nonlinear Sci. Numer. Simulat., 22 (1–3) (2015), pp. 650-659.
B.K. Mishra and D.K. Saini, “SEIRS epidemic model with delay for transmission of malicious objects in computer network”, Appl. Math. Comput., 188 (2) (2007), pp. 1476-1482.
B.K. Mishra and N. Keshri, “Mathematical model on the transmission of worms in wireless sensor network”, Appl. Math. Model., 37 (6) (2013), pp. 4103-4111.
M. Di Paola, A. Pirrotta and A. Valenza, “Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results”, Mech. Mater., 43 (12) (2011), pp. 799-806.
T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control”, IEEE Trans. Syst., Man, Cybern., 15 (1) (1985), pp. 116–132.
H. M. Tuan and P.H. Thu, “Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses”, Journal of Science and Technology on Information Security, 3 (17) (2023), pp. 17-25.
T.A. Tuan, N.N. Cuong, N. V. Anh and H.V. Long, “Proposing the application of a deep learning model to detect the malicious IP address of botnet in the computer network”, Journal of Science and Technology on Information Security, 3 (17) (2023), pp. 43-52.
L.X. Yang, M. Draief and X. Yang, “The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model”, Phys. A, 450 (2016), pp. 403-415.
X. Zhang, Z. Cheng and Q. Liu, “A fuzzy logic approach to optimal control of nonlinear time-delay systems}, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788), (1) (2004), pp. 902-906.
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