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Observer-based security control for Markov jump systems under hybrid cyber-attacks and its application via event-triggered scheme

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Abstract

This article investigates the observer-based security control of discrete-time Markov jump systems (MJSs) subject to hybrid cyber-attacks and unmeasured states via event-triggered scheme. The event-triggered scheme (ETS) is being developed to relieve more network burdens. A Luenburger observer is used to estimate the unmeasured states. In this work, the hybrid cyber attack is addressed, which contains deception attacks and DoS attacks. It is anticipated that input control signals sent across a network are vulnerable to hybrid cyber-attacks in which adversaries could inject fake data into the control signals. Since system state information is usually not fully known, an observer-based controller is built to stabilize the system and keep the right performance index even when hybrid cyber-attacks happen. By solving linear matrix inequalities (LMIs), the controllers and observers are also obtained. Lastly, inverted pendulum applications are shown to show how well and realistically the theoretical results can be used to respond to and get rid of the effects of hybrid cyber-attacks.

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References

  • Alshdadi AA (2021) Cyber-physical system with IoT-based smart vehicles. IEEE Trans Cybern 25:12261–12273

    Google Scholar 

  • Cao J, Ding D, Liu J, Tian E, Hu S, Xie X (2021) Hybrid-triggered-based security controller design for networked control system under multiple cyber attacks. Inf Sci 548:69–84

    Article  MathSciNet  Google Scholar 

  • Deng C, Wen C (2022) Event-triggered remote state estimation for cyber-physical systems under malicious DoS attacks. Inf Sci 602:43–56

    Article  Google Scholar 

  • Deng Y, Lu H, Zhou W (2021) Security event-triggered control for Markovian jump neural networks against actuator saturation and hybrid cyber attacks. J Franklin Inst 358(14):7096–7118

    Article  MathSciNet  Google Scholar 

  • Dong Z, Wang X, Zhang X (2020) A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen-Grossberg neural networks. Appl Math Comput 385:125401

    Article  MathSciNet  Google Scholar 

  • Elhaleem SA, Soliman M, Hamdy M (2022) Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems. Soft Comput 26:6461–6462

    Article  Google Scholar 

  • Fuentes R, Oliveira PM, Carvalho LP, Lacerda MJ, Palma JM (2022) Autonomous vehicle platoon packet based control problem under Denial-of-Service attacks. In: APCA international conference on automatic control and soft computing, pp 474–486

  • Gao X, Deng F, Zeng P, Zhang H (2023) Adaptive neural event-triggered control of networked Markov jump systems under hybrid cyber-attacks. IEEE Trans Neural Netw Learn Syst 34(3):1502–1512

    Article  MathSciNet  PubMed  Google Scholar 

  • Ge X, Yang F, Han QL (2017) Distributed networked control systems: a brief overview. Inf Sci 380:117–131

    Article  ADS  Google Scholar 

  • Guo L, Yu H, Hao F (2020) Event-triggered control for stochastic networked control systems against denial-of-service attacks. Inf Sci 527:51–69

    Article  MathSciNet  Google Scholar 

  • Hao F, Zhao X (2010) Linear matrix inequality approach to static output-feedback stabilisation of discrete-time networked control systems. IET Control Theory Appl 4(7):1211–1221

    Article  MathSciNet  Google Scholar 

  • Hu S, Gu Y, Chen X, Ge H (2018) Observer-based event-triggered control for cyber-physical systems under unknown periodic DoS jamming attacks. In: Chinese control and decision conference (CCDC), pp 1422–1427

  • Kashyap N, Malali HRK, Gururaj HL (2020) Cyber attacks and security—a critical survey. In: Soft computing: theories and applications, pp 895–994

  • Kumar P, Dudeja C (2021) Shadowed type 2 fuzzy-based Markov model to predict shortest path with optimized waiting time. Soft Comput 25:995–1005

    Article  Google Scholar 

  • Li F, Fu J, Du D (2016) An improved event-triggered communication mechanism and \(L_{\infty }\) control co-design for network control systems. Inf Sci 370:743–762

    Article  Google Scholar 

  • Lian Z, Shi P, Lim CC (2021) Hybrid-triggered interval type-2 fuzzy control for networked systems under attacks. Inf Sci 567:332–347

    Article  MathSciNet  Google Scholar 

  • Lin Y, Zhuang G, Xia J, Sun W, Zhao J (2022) Asynchronous \(H_{\infty }\) dynamic output feedback control for Markovian jump neural networks with time-varying delays. Int J Control Autom Syst 20:909–923

    Article  Google Scholar 

  • Liu J, Wu H (2022) Global fixed-time synchronization for coupled time-varying delayed neural networks with multi-weights and uncertain couplings via periodically semi-intermittent adaptive control. Soft Comput 26:1685–1702

    Article  Google Scholar 

  • Liu J, Gu Y, Zha L, Liu Y, Cao J (2016) Event-triggered \(H_{\infty }\) load frequency control for multiarea power systems under hybrid cyber attacks. IEEE Trans Syst Man Cybern Syst 49(8):1665–1678

    Article  CAS  Google Scholar 

  • Liu J, Wei L, Tian E, Fei S, Cao J (2017) \(H_{\infty }\) filtering for networked systems with hybrid-triggered communication mechanism and stochastic cyber attacks. J Franklin Inst 354(18):8490–8512

    Article  MathSciNet  Google Scholar 

  • Liu J, Yin T, Xie X, Tian E, Fei S (2019a) Event-triggered state estimation for T-S fuzzy neural networks with stochastic cyber-attacks. Int J Fuzzy Syst 21:532–544

    Article  MathSciNet  Google Scholar 

  • Liu J, Gu Y, Xie X, Yue D, Park JH (2019b) \(H_{\infty }\) control for networked cascade control systems with actuator saturations and stochastic cyber attacks. IEEE Trans Syst Cybern 49(12):2452–2463

    Google Scholar 

  • Liu Y, Zhi H, Wei J, Zhu X, Zhu Q (2020a) Event-triggered control for linear continuous switched singular systems. Appl Math Comput 374(1):125038

    Article  MathSciNet  Google Scholar 

  • Liu J, Yin T, Cao J, Yue D, Karimi HR (2020b) Security control for T-S fuzzy systems with adaptive event-triggered mechanism and multiple cyber-attacks. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/ACCESS.2020.3043238

    Article  Google Scholar 

  • Luo J, Tian W, Zhong S, Shi K, Wang W (2018) Non-fragile asynchronous event-triggered control for uncertain delayed switched neural networks. Nonlinear Anal Hybrid Syst 29:54–73

    Article  MathSciNet  Google Scholar 

  • Mousavi A, Aryankia K, Selmic RR, Xie X (2022) A distributed FDI cyber-attack detection in discrete-time nonlinear multi-agent systems using neural networks. Eur J Control 66:100646

    Article  MathSciNet  Google Scholar 

  • Nagamani G, Soundararajan G, Subramaniam R, Azeem M (2020a) Robust extended dissipativity analysis for Markovian jump discrete-time delayed stochastic singular neural networks. Neural Comput Appl 32:9699–9712

    Article  Google Scholar 

  • Nagamani G, Karthik C, Joo YH (2020b) Event-triggered observer-based sliding mode control for T-S fuzzy systems via improved relaxed-based integral inequality. J Franklin Inst 357(14):9543–9567

    Article  MathSciNet  Google Scholar 

  • Padmaja N, Balasubramaniam P (2022) Results on passivity and design of passive controller for fuzzy neural networks with additive time-varying delays. Soft Comput 26:9911–9925

    Article  Google Scholar 

  • Sahoo A, Xu H, Jagannathan S (2015) Adaptive neural network-based event-triggered control of single-input single-output nonlinear discrete-time systems. IEEE Trans Neural Netw Learn Syst 27(1):151–164

    Article  MathSciNet  PubMed  Google Scholar 

  • Shen H, Su L, Park JuH (2016) Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays. Signal Process 128:68–77

    Article  Google Scholar 

  • Shi Y, Yu B (2009) Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans Autom Control 54(7):1868–1874

    MathSciNet  Google Scholar 

  • Suryaprabha E, Kumar NMS (2020) Enhancement of security using optimized DoS (denial-of-service) detection algorithm for wireless sensor network. Soft Comput 24:10681–10691

    Article  Google Scholar 

  • Syed Ali M, Vadivel R, Alsaedi A, Ahmad B (2020) Extended dissipativity and event-triggered synchronization for T-S fuzzy Markovian jumping delayed stochastic neural networks with leakage delays via fault-tolerant control. Soft Comput 24:3675–3694

    Article  Google Scholar 

  • Tajudeen MM, Ali MS, Kauser SA, Subkrajang K, Jirawattanapanit A, Rajchakit G (2022) Adaptive event-triggered control for complex dynamical network with random coupling delay under stochastic deception attacks. Hindawi Complex 2022:8761612

    Google Scholar 

  • Vadivel R, Ali MS, Joo YH (2020) Event-triggered \(H_\infty \) synchronization for switched discrete time delayed recurrent neural networks with actuator constraints and nonlinear perturbations. J Franklin Inst 357(7):4079–4108

    Article  MathSciNet  Google Scholar 

  • Val JD, Nespoli C, Caceres RY (2003) Stochastic stability for Markovian jump linear systems associated with a finite number of jump times. J Math Anal Appl 285(2):551–563

    Article  MathSciNet  Google Scholar 

  • Wang B, Zhu Q (2020) Stability analysis of discrete-time semi-Markov jump linear systems with partly unknown semi-Markov kernel. Syst Control Lett 140:104688

    Article  MathSciNet  Google Scholar 

  • Wang H, Xue A, Wang J, Lu R (2017) Event-based \(H_{\infty }\) filtering for discrete-time Markov jump systems with network-induced delay. J Franklin Inst 354(14):6170–6189

    Article  MathSciNet  Google Scholar 

  • Wang Z, Xu X, Sun H, Li L (2020) Dual-terminal event triggered control for cyber-physical systems under false data injection attacks. Kybernetika 56(2):323–339

    MathSciNet  CAS  Google Scholar 

  • Wang T, Zhang B, Yuan D, Zhang Y (2021) Event-based extended dissipative state estimation for memristor-based Markovian neural networks with hybrid time-varying delays. IEEE Trans Circuits Syst I Regul Pap 68(11):4520–4533

    Article  Google Scholar 

  • Wu Z, Xiong J, Xie M (2021) Dynamic event-triggered \(L_{\infty }\) control for networked control systems under deception attacks: a switching method. Inf Sci 561:168–180

    Article  Google Scholar 

  • Zeng F, Wang Y, Zhuang G, Chen F (2022) Dynamic-memory event-triggered-based controller design for singular stochastic semi-Markov jump systems against multiple cyber-attacks. Nonlinear Dyn 110:1559–1582

    Article  Google Scholar 

  • Zhang L, Shi Y, Chen T, Huang B (2005) A new method for stabilization of networked control systems with random delays. IEEE Trans Autom Control 50:1177–1181

    Article  MathSciNet  Google Scholar 

  • Zhang W, Li J, Xing K, Zhang R, Zhang X (2021a) Event-triggered synchronization of uncertain delayed generalized RDNNs. Soft Comput 25:13243–13261

    Article  Google Scholar 

  • Zhang Y, Zhao B, Liu D (2021b) Event-triggered adaptive dynamic programming for multi-player zero-sum games with unknown dynamics. Soft Comput 25:2237–2251

    Article  Google Scholar 

  • Zhang XM, Han Q-L, Ge X (2022) A novel approach to \(H_{\infty }\) performance analysis of discrete-time networked systems subject to network-induced delays and malicious packet dropouts. Automatica 136:110010

  • Zheng W, Zhang Z, Sun F, Wen S (2022) Robust stability analysis and feedback control for networked control systems with additive uncertainties and signal communication delay via matrices transformation information method. Inf Sci 582:258–286

    Article  MathSciNet  Google Scholar 

  • Zhou Q, Shi P, Xu S, Li H (2012) Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans Neural Netw Learn Syst 24(1):71–80

    Article  Google Scholar 

  • Zhu X, Zhang X, Wei J, Du H, Xi J (2022) Dynamic event-triggered control of networked control systems with uncertainty and transmission delay. J Franklin Inst 359:477–491

  • Zubi AAA, Maitah MA, Alarifi A (2021) Cyber-attack detection in healthcare using cyber-physical system and machine learning techniques. Soft Comput 25(18):12319–12332

    Article  Google Scholar 

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Acknowledgements

The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia has funded this project under grant no. FP-131-43.

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Authors and Affiliations

  1. Complex Systems and Networked Science Lab, Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, 632 115, India

    M. Mubeen Tajudeen & M. Syed Ali

  2. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai, Tamil Nadu, 603 203, India

    R. Perumal

  3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, Saudi Arabia

    Hamed Alsulami & Bashir Ahmad

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  1. M. Mubeen Tajudeen
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  2. M. Syed Ali
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  5. Bashir Ahmad
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Correspondence to R. Perumal.

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Tajudeen, M.M., Ali, M.S., Perumal, R. et al. Observer-based security control for Markov jump systems under hybrid cyber-attacks and its application via event-triggered scheme. Soft Comput 28, 5155–5171 (2024). https://doi.org/10.1007/s00500-023-09234-1

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