A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 6
Oct.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 11.8, Top 4% (SCI Q1)
    CiteScore: 17.6, Top 3% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Lei Liu, Lifeng Ma, Jie Zhang and Yuming Bo, "Sliding Mode Control for Nonlinear Markovian Jump Systems Under Denial-of-Service Attacks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1638-1648, Nov. 2020. doi: 10.1109/JAS.2019.1911531
Citation: Lei Liu, Lifeng Ma, Jie Zhang and Yuming Bo, "Sliding Mode Control for Nonlinear Markovian Jump Systems Under Denial-of-Service Attacks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1638-1648, Nov. 2020. doi: 10.1109/JAS.2019.1911531

Sliding Mode Control for Nonlinear Markovian Jump Systems Under Denial-of-Service Attacks

doi: 10.1109/JAS.2019.1911531
Funds:  This work was supported in part by the National Natural Science Foundation of China (61773209), the Six Talent Peaks Project in Jiangsu Province (XYDXX-033), the Postdoctoral Science Foundation of China (2014M551598), and the Natural Science Foundation of Jiangsu Province (BK20190021)
More Information
  • This paper investigates the sliding mode control (SMC) problem for a class of discrete-time nonlinear networked Markovian jump systems (MJSs) in the presence of probabilistic denial-of-service (DoS) attacks. The communication network via which the data is propagated is unsafe and the malicious adversary can attack the system during state feedback. By considering random Denial-of-Service attacks, a new sliding mode variable is designed, which takes into account the distribution information of the probabilistic attacks. Then, by resorting to Lyapunov theory and stochastic analysis methods, sufficient conditions are established for the existence of the desired sliding mode controller, guaranteeing both reachability of the designed sliding surface and stability of the resulting sliding motion. Finally, a simulation example is given to demonstrate the effectiveness of the proposed sliding mode control algorithm.

     

  • loading
  • [1]
    E. Boukas, Stochastic Switching Systems: Analysis and Design, Boston, MA: Birkhauser, 2006.
    [2]
    P. Shi, M. Mahmoud, S. K. Nguang, and A. Ismail, “Robust filtering for jumping systems with mode-dependent delays,” Signal Processing, vol. 86, no. 1, pp. 140–152, 2006. doi: 10.1016/j.sigpro.2005.05.005
    [3]
    R. Sakthivel, H. R. Karimi, M. Joby, and S. Santra, “Resilient sampleddata control for Markovian jump systems with an adaptive fault-tolerant mechanism,” IEEE Trans. Circuits and Systems Ⅱ−Express Briefs, vol. 64, no. 11, pp. 1312–1316, 2017. doi: 10.1109/TCSII.2017.2669102
    [4]
    L. G. Wu, P. Shi, and H. J. Gao, “State estimation and sliding-mode control of Markovian jump singular systems,” IEEE Trans. Autom. Control, vol. 55, pp. 1213–1219, 2010. doi: 10.1109/TAC.2010.2042234
    [5]
    Y. Song, H. F. Lou, and S. Liu, “Distributed model predictive control with actuator saturation for Markovian jump linear system,” IEEE/CAA J. Autom. Sinica, vol. 2, no. 4, pp. 374–381, Oct. 2015. doi: 10.1109/JAS.2015.7296532
    [6]
    R. Saravanakumar, M. S. Ali, and H. R. Karimi, “Robust H control of uncertain stochastic Markovian jump systems with mixed time-varying delays,” Int. J. Systems Science, vol. 48, no. 4, pp. 862–872, 2017. doi: 10.1080/00207721.2016.1218092
    [7]
    Y. G. Niu, D. W. C. H. Ho, and X. Y. Wang, “Sliding mode control for Ito stochastic systems with Markovian switching,” Automatica, vol. 43, no. 10, pp. 1784–1790, 2007. doi: 10.1016/j.automatica.2007.02.023
    [8]
    Y. G. Kao, W. Li, and C. H. Wang, “Nonfragile observer-based H sliding mode control for Ito stochastic systems with Markovian switching,” Int. J. Robust and Nonlinear Control, vol. 24, no. 15, pp. 2035–2047, 2014. doi: 10.1002/rnc.v24.15
    [9]
    O. L. V. Costa and R. P. Marques, “Mixed H2/H control of discretetime Markovian jump linear systems,” IEEE Trans. Autom. Control, vol. 43, no. 1, pp. 95–100, 1998. doi: 10.1109/9.654895
    [10]
    J. L. Xiong and J. Lam, “Robust H2 control of Markovian jump systems with uncertain switching probabilities,” Int. J. Systems Science, vol. 40, no. 3, pp. 255–265, 2009. doi: 10.1080/00207720802300347
    [11]
    W. B. Gao, Y. F. Wang, and A. Homaifa, “Discrete-time variable structure control systems,” IEEE Trans. Industrial Electronics, vol. 42, no. 2, pp. 117–122, 1995. doi: 10.1109/41.370376
    [12]
    L. F. Ma, Z. D. Wang, and H. K. Lam, “Event-triggered mean-square consensus control for time-varying stochastic multi-agent system with sensor saturations,” IEEE Trans. Autom. Control, vol. 62, no. 7, pp. 3524–3531, 2017. doi: 10.1109/TAC.2016.2614486
    [13]
    S. L. Sun, L. H. Xie, and W. D. Xiao, “Optimal full-order and reduced-order estimators for discrete-time systems with multiple packet dropouts,” IEEE Trans. Signal Processing, vol. 56, no. 8, pp. 4031–4038, 2008. doi: 10.1109/TSP.2008.923196
    [14]
    M. S. Mahmoud and M. S. U. Rahman, “Networked control approach for distributed generation systems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 836–851, 2018. doi: 10.1109/JAS.2017.7510688
    [15]
    X. Zhu, C. Hua, and S. Wang, “State feedback controller design of networked control systems with time delay in the plant,” Int. J. Innovative Computing,Information and Control, vol. 4, no. 2, pp. 283–290, 2008.
    [16]
    Z. H. Wang, J. J. Xu, and H. S. Zhang, “Consensus seeking for discrete-time multi-agent systems with communication delay,” IEEE/CAA J. Autom. Sinica, vol. 2, no. 2, pp. 151–157, Apr. 2015. doi: 10.1109/JAS.2015.7081654
    [17]
    D. R. Ding, Z. D. Wang, B. Shen, and H. L. Dong, “H state estimation with fading measurements, randomly varying nonlinearities and probabilistic distributed delays,” Int. J. Robust and Nonlinear Control, vol. 25, no. 13, pp. 2180–2195, 2015. doi: 10.1002/rnc.v25.13
    [18]
    H. L. Dong, J. Lam, and H. J. Gao, “Distributed H1 filtering for repeated scalar nonlinear systems with random packet losses in sensor networks,” Int. J. Systems Science, vol. 52, no. 11, pp. 1507–1519, 2011.
    [19]
    H. J. Gao and T. W. Chen, “H estimation for uncertain systems with limited communication capacity,” IEEE Trans. Autom. Control, vol. 52, no. 11, pp. 2070–2084, 2007. doi: 10.1109/TAC.2007.908316
    [20]
    E. G. Tian, D. Yue, and C. Peng, “Quantized output feedback control for networked control systems,” Information Sciences, vol. 178, pp. 2734–2749, 2008. doi: 10.1016/j.ins.2008.01.019
    [21]
    J. F. Wang and C. F. Liu, “Stabilization of uncertain systems with Markovian modes of time delay and quantization density,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 463–470, Mar. 2018. doi: 10.1109/JAS.2017.7510823
    [22]
    B. Chen, Y. G. Niu, and Y. Y. Zou, “Sliding mode control for stochastic Markovian jumping systems subject to successive packet losses,” J. Franklin Institue-Engineering and Applied Mathematics, vol. 351, no. 4, pp. 2169–2184, 2014. doi: 10.1016/j.jfranklin.2012.10.004
    [23]
    Y. G. Niu and D. W. C. Hu, “Design of sliding mode control subject to packet losses,” IEEE Trans. Autom. Control, vol. 55, no. 11, pp. 2623–2628, 2010. doi: 10.1109/TAC.2010.2069350
    [24]
    B. C. Zheng and G. H. Yang, “Robust quantized feedback stabilization of linear systems based on sliding mode control,” Optimal Control Application and Methods, vol. 34, no. 4, pp. 458–471, 2013. doi: 10.1002/oca.v34.4
    [25]
    M. M. Rana, L. Li, and S. W. Su, “Cyber attack protection and control of microgrids,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 2, pp. 602–609, Mar. 2018. doi: 10.1109/JAS.2017.7510655
    [26]
    S. Amin, G. A. Schwartz, and S. S. Sastry, “Security of interdependent and identical networked control systems,” Automatica, vol. 49, no. 1, pp. 186–192, 2013. doi: 10.1016/j.automatica.2012.09.007
    [27]
    Y. M. Wu and X. X. He, “Secure consensus control for multi-agent systems with attacks and communication delays,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 136–142, Jan. 2017. doi: 10.1109/JAS.2016.7510010
    [28]
    H. Fawzi, P. Tabuada, and S. Diggavi, “Secure estimation and control for cyber-physical systems under adversarial attacks,” IEEE Trans. Autom. Control, vol. 59, no. 6, pp. 1454–1467, 2014. doi: 10.1109/TAC.2014.2303233
    [29]
    D. R. Ding, Z. D. Wang, G. L. Wei, and F. E. Alsaadi, “Event-based security control for discrete-time stochastic systems,” IET Control Theory and Application, vol. 10, no. 15, pp. 1808–1815, 2016. doi: 10.1049/iet-cta.2016.0135
    [30]
    Z. Feng, G. Q. Hu, and G. H. Wen, “Distributed consensus tracking for multiagent systems under two types of attacks,” Int. J. Robust and Nonlinear Control, vol. 26, no. 5, pp. 896–918, 2016. doi: 10.1002/rnc.v26.5
    [31]
    M. Long, C. H. Wu, and J. Y. Hung, “Denial of service attacks on network-based control systems: Impact and mitigation,” IEEE Trans. Industrial Informatics, vol. 1, no. 2, pp. 85–96, 2005. doi: 10.1109/TII.2005.844422
    [32]
    L. F. Ma, Z. D. Wang, Q. L. Han, and H. K. Lam, “Variance-constrained distributed filtering for time-varying systems with multiplicative noises and deception attacks over sensor networks,” IEEE Sensors J, vol. 17, no. 7, pp. 2279–2288, 2017. doi: 10.1109/JSEN.2017.2654325
    [33]
    S. Amin, A. A. Cardenas, and S. S. Sastry, “Safe and secure networked control systems under denial-of-service attacks,” in Proc. 12th Int. Conf. Hybrid Systems − Computation and Control, San Francisco, CA, USA, Apr. 2009, pp. 31−45.
    [34]
    B. Chen, L. Yu, D. W. C. Ho, and W. A. Zhang, “Networked fusion estimation under Denial-of-Service attacks,” in Proc. 20th World Congress of the International-Federation-of-Automatic-Control (IFAC), Toulouse, France, Jul. 2017, pp. 3835−3840.
    [35]
    A. Gupta, C. Langbort, and T. Basar, “Optimal control in the presence of an intelligent jammer with limited actions,” in Proc. 49th IEEE Conf. Decision and Control, Atlanta, GA, USA, Dec. 2010, pp. 1096−1101.
    [36]
    H. Zhang and W. X. Zheng, “Denial-of-service power dispatch against linear quadratic control via a fading channel,” IEEE Trans. Autom. Control, vol. 63, no. 9, pp. 3032–3039, 2018. doi: 10.1109/TAC.2018.2789479
    [37]
    L. H. Peng, L. Shi, X. H. Cao, and C. Y. Sun, “Optimal attack energy allocation against remote state estimation,” IEEE Trans. Autom. Control, vol. 63, no. 7, pp. 2199–2205, 2018. doi: 10.1109/TAC.2017.2775344
    [38]
    Y. Yaz and E. Yaz, “On LMI formulations of some problems arising in nonlinear stochastic system analysis,” IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 813–816, 1999. doi: 10.1109/9.754824
    [39]
    F. W. Yang, Z. D. Wang, D. W. C. Ho, and X. H. Liu, “Robust H2 filtering for a class of systems with stochastic nonlinearities,” IEEE Trans. Circuits Systems − Part Ⅱ, vol. 53, no. 3, pp. 235–239, 2006. doi: 10.1109/TCSII.2005.858492
    [40]
    H. L. Dong, Z. D. Wang, J. Lam, and H. J. Gao, “Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts,” IEEE Trans. Systems,Man,and Cybernetics Part B−Cybernetics, vol. 42, no. 2, pp. 365–376, 2012. doi: 10.1109/TSMCB.2011.2163797
    [41]
    S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadephia: SIAM, 1994.
    [42]
    J. Zhang, Z. D. Wang, D. R. Ding, and X. H. Liu, “H state estimation for discrete-time delayed neural networks with randomly occurring quantizations and missing measurements,” Neurocomputing, vol. 148, pp. 388–396, 2015. doi: 10.1016/j.neucom.2014.06.017
    [43]
    L. F. Ma, Z. D. Wang, Y. M. Bo, and Z. Guo, “Robust H sliding mode control for nonlinear stochastic systems with multiple data packet losses,” Int. J. Robust Nonlinear Control, vol. 22, no. 5, pp. 473–491, 2012. doi: 10.1002/rnc.v22.5

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(6)

    Article Metrics

    Article views (1300) PDF downloads(101) Cited by()

    Highlights

    • A new sliding mode variable is constructed, containing the message of DoS attack.
    • A sliding mode control algorithm is developed under DoS attack.
    • The developed sliding mode control algorithm can effectively deal with DoS attack.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return