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Finite-time boundedness and dissipativity analysis of networked cascade control systems

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Abstract

In this paper, finite-time boundedness and dissipativity analysis for a class of networked cascade control systems (NCCSs) is investigated. The NCCS is defined with network-induced imperfections such as packet dropouts and time delays, and Bernoulli distributed white sequence is used to model a stochastic packet dropout case. Using the Lyapunov stability theory and linear matrix inequality (LMI) approach, we propose the sufficient conditions for finite-time boundedness and finite-time dissipativity of NCCS. Finally, the LMI-based conditions are applied on a practical power plant boiler–turbine system to show the effectiveness and applicability of the achieved results.

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References

  1. Franks, R., Worley, C.: Quantitative analysis of cascade control. Ind. Eng. Chem. 48, 1074–1079 (1956)

    Article  Google Scholar 

  2. Du, Z., Yue, D., Hu, S.: H-infinity stabilization for singular networked cascade control systems with state delay and disturbance. IEEE Trans. Ind. Inf. 10, 1551–3203 (2014)

  3. Huang, C., Bai, Y., Liu, X.: H-infinity state feedback control for a class of networked cascade control systems with uncertain delay. IEEE Trans. Ind. Inf. 6, 62–72 (2010)

    Article  Google Scholar 

  4. Wai, R., Kuo, M., Lee, J.: Design of cascade adaptive fuzzy sliding-mode control for nonlinear two-axis inverted-pendulum servomechanism. IEEE Trans. Fuzzy Syst. 16, 1232–1244 (2008)

    Article  Google Scholar 

  5. Guo, C., Song, Q., Cai, W.: A neural network assisted cascade control system for air handling unit. IEEE Trans. Ind. Electron. 54, 620–628 (2007)

    Article  Google Scholar 

  6. Demirel, B., Briat, C., Johansson, M.: Deterministic and stochastic approaches to supervisory control design for networked systems with time-varying communication delays. Nonlinear Anal. Hybrid Syst. 10, 94–110 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mathiyalagan, K., Lee, T.H., Park, J.H., Sakthivel, R.: Robust passivity based resilient \({\cal {H}}_{\infty }\) control for networked control systems with random gain fluctuations. Int. J. Robust Nonlinear Control 26, 426–444 (2016)

  8. Mathiyalagan, K., Park, J.H., Jung, H.Y., Sakthivel, R.: Non-fragile observer-based \({\cal {H}}_{\infty }\) control for discrete-time systems using passivity theory. Circuits Syst. Signal Proc. 34, 2499–2516 (2015)

  9. Millan, P., Orihuela, L., Vivas, C., Rubio, F.R.: Distributed consensus-based estimation considering network induced delays and dropouts. Automatica 48, 2726–2729 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, W.A., Yu, L., Yin, S.: A switched system approach to \({\cal {H}}_{\infty }\) control of networked control systems with time-varying delays. J. Frankl. Inst. 348, 165–178 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fadaei, A., Salahshoor, K.: Evaluation study of the transmission delay effects in a practical networked cascade control system. In: Proceedings of 16th Mediterranean Conference on Control and Automation Congress Centre, France, pp. 1598–1603 (2008)

  12. Lee, T.H., Park, J.H., Lee, S.M., Kwon, O.M.: Robust sampled-data control with random missing data scenario. Int. J. Control 87, 1957–1969 (2014)

  13. Zhang, W.A., Yu, L.: Modelling and control of networked control systems with both network-induced delay and packet-dropout. Automatica 44, 3206–3210 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, C., Feng, G., Qiu, J., Shen, Y.: Control synthesis for a class of linear network-based systems with communication constraints. IEEE Trans. Ind. Electron. 60, 3339–3348 (2013)

    Google Scholar 

  15. Yang, H., Knag, Y., Kuang, S.: Predictive compensation for networked cascade control systems with uncertainties. In: Proceedings of 31st Chinese Control Conference, Hefei, pp. 4256–4260 (2012)

  16. Luo, W., Soares, C.G., Zou, Z.: Neural-network- and \({\cal {L}}_2\)-gain-based cascaded control of underwater robot thrust. IEEE J. Oceanic Eng. 39, 630–640 (2014)

  17. Kottenstette, N., Hall III, J.F., Koutsoukos, X., Sztipanovits, J., Antsaklis, P.: Design of networked control systems using passivity. IEEE Trans. Control Syst. Technol. 21, 649–665 (2013)

    Article  Google Scholar 

  18. Willems, J.C.: Dissipative dynamical systems-part 1: general theory. Arch. Ration. Mech. Anal. 45, 321–351 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  19. Willems, J.C.: Dissipative dynamical systems-part 2: linear systems with quadratic supply rates. Arch. Ration. Mech. Anal. 45, 352–393 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hill, D.J., Moylan, P.J.: Stability of nonlinear dissipative systems. IEEE Trans. Autom. Control 21, 708–711 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hill, D.J., Moylan, P.J.: Dissipative dynamical systems: basic input–output and state properties. J. Frankl. Inst. 309, 327–357 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Shen, H., Wu, Z.G., Park, J.H.: Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts. IET Control Theory Appl. 8, 1617–1624 (2014)

  23. Wang, S., Shi, T., Zhang, L., Jasra, A., Zeng, M.: Extended finite-time \({\cal {H}}_{\infty }\) control for uncertain switched linear neutral systems with time-varying delays. Neurocomputing 152, 377–387 (2015)

  24. Yin, J., Khoo, S., Man, Z., Yu, X.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47, 2671–2677 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zuo, Z., Li, H., Wang, Y.: New criterion for finite-time stability of linear discrete-time systems with time-varying delay. J. Frankl. Inst. 350, 2745–2756 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu, H., Zhao, X., Zhang, H.: New approaches to finite-time stability and stabilization for nonlinear system. Neurocomputing 138, 218–228 (2014)

    Article  Google Scholar 

  27. Du, H., Cheng, Y., He, Y., Jia, R.: Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters. Nonlinear Dyn. 78, 2021–2030 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang, H., Han, Z., Xie, Q., Zhang, W.: Finite-time chaos control of unified chaotic systems with uncertain parameters. Nonlinear Dyn. 55, 323–328 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Shen, H., Park, J.H., Wu, Z.G.: Finite-time reliable \(L_2\)-\(L_{\infty }/{\cal {H}}_{\infty }\) control for Takagi–Sugeno fuzzy systems with actuator faults. IET Control Theory Appl. 8, 688–696 (2014)

    Article  MathSciNet  Google Scholar 

  30. Zhang, Y., Shi, P., Nguang, S.K.: Observer-based finite-time \({\cal {H}}_{\infty }\) control for discrete singular stochastic systems. Appl. Math. Lett. 38, 115121 (2014)

    MathSciNet  Google Scholar 

  31. Li, S., Tian, Y.P.: Finite-time stability of cascaded time-varying systems. Int. J. Control 80, 646–657 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Huang, C., Bai, Y., Li, X.: Fundamental issues in networked cascade control systems. In: Proceedings of the IEEE International Conference on Automation and Logistics, Qingdao, pp. 314–3018 (2008)

  33. Boyd, B., Ghoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    Book  Google Scholar 

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Acknowledgments

The work of K. Mathiyalagan was supported by University Grants Commission (UGC), New Delhi, India, through Dr. D. S. Kothari Postdoctoral Fellowship under the Grant No. F.42/2006 (BSR)/MA/1415/0003, and the work of J. H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A 10005201).

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Authors and Affiliations

  1. Department of Mathematics, Bharathiyar University, Coimbatore, 641 046, India

    K. Mathiyalagan

  2. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 38541, Republic of Korea

    Ju H. Park

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440 746, Republic of Korea

    R. Sakthivel

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  1. K. Mathiyalagan
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  2. Ju H. Park
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  3. R. Sakthivel
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Correspondence to Ju H. Park or R. Sakthivel.

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Mathiyalagan, K., Park, J.H. & Sakthivel, R. Finite-time boundedness and dissipativity analysis of networked cascade control systems. Nonlinear Dyn 84, 2149–2160 (2016). https://doi.org/10.1007/s11071-016-2635-2

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  • DOI: https://doi.org/10.1007/s11071-016-2635-2

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