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A Cyber-Security Contribution to Estimation and Event-Based Control Scheduling Co-design for Polytopic and T-S Fuzzy Models Using a Lyapunov Approach

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Abstract

In the present contribution, a focus is given to the state and cyber-physical attacks reconstruction for a class of nonlinear systems. The proposed approach is based on the polytopic fuzzy representation of the system coupled with an event-based scheduling (sample-and-hold strategy) co-design. The considered attacks are of the type of data-deception, and affect both sensors and actuators. The polytopic fuzzy strategy has been chosen to incorporate the triggering condition in the control design itself and have a unified and a single problem to deal with.

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References

  1. Yacef, F., Bouhali, O., Khebbache, H., Boudjema, F.: Takagi-Sugeno model for quadrotor modeling and control using nonlinear state feedback controller. Int. J. Control Theory Comput. Model. 2, 9–24 (2012)

    Google Scholar 

  2. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  Google Scholar 

  3. Tanaka, K., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Ed Hardcover. Wiley, New York (2001)

    Book  Google Scholar 

  4. Sugeno, M., Kang, G.: Structure identification of fuzzy model. Fuzzy Sets Syst 15–33 (1988)

  5. Tanaka, K., Ikeda, T., Wang, H.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI based designs. IEEE Trans. Fuzzy Syst. 6(2), 250–265 (1998)

    Article  Google Scholar 

  6. Tanaka, K., Hori, T., Wang, H.: A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE Trans. Fuzzy Syst. 11, 582–589 (2003)

    Article  Google Scholar 

  7. Sheng, Z., Wang, L., Lin, C., et al.: A novel asymmetric Lyapunov-Krasovskii functional method to stability for T-S fuzzy systems with time-varying delay. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-021-01176-w

    Article  Google Scholar 

  8. Angelis, G.Z.: System analysis, modelling and control with polytopic linear models, PhD thesis. Eindhoven Technische Universiteit, Eindhoven (2001)

  9. Chadli, M., Maquin, D., Ragot, J.: Static output feedback for Takagi-Sugeno systems: an LMI approach. In: 10th Mediterranean Conference on Control and Automation, Lisbon, Portugal (2002)

  10. Guerra, T., Kruszewski, A., Vermeiren, L., Tirmant, H.: Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form. Fuzzy Sets Syst. 157, 1248–1259 (2006)

    Article  MathSciNet  Google Scholar 

  11. Kruszewski, A., Wang, R., Guerra, T.M.: Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach. IEEE Trans. Autom. Control 53, 606–611 (2008)

    Article  MathSciNet  Google Scholar 

  12. Bezzaoucha, S., Marx, B., Maquin, D., Ragot, J.: Nonlinear joint state and parameter estimation. Application to a wastewater treatment plant. Control Eng. Pract. 1377–1385 (2013)

  13. Bezzaoucha, S., Voos, H., Darouach, M.: A Contribution to Cyber-Security of Networked Control Systems: an Event-based Control Approach in \(3^{rd}\) International Conference on Event-Based Control, Communication and Signal Processing. Funchal, Madeira, Portugal (2017)

  14. Murray-Smith, R., Johansen, T.: Multiple Model Approaches to Modelling and Control. Taylor and Francis, Milton Park (1997)

    Google Scholar 

  15. Sontag, E.: Mathematical Control Theory. Text in Applied Mathematics. Springer, New York (1998)

    Book  Google Scholar 

  16. Kalman, R., Falb, P., Arbib, M.: Topics in Mathematical System Theory. In Mathematical System Theory. International Series in Pure and and Applied Mathematics. McGraw-Hill Book Company (1969)

  17. Cervin, A., Henningsson: scheduling of event-triggered controllers on a shared NETWORK in 47th IEEE Conference Decision and Control CDC, Cancun, Mexico (2008)

  18. Al-Areqi, S., Gorges, D., Liu, S.: Event-based control and scheduling codesign: stochastic and robust approaches. IEEE Trans. Autom. Control 60, 1291–1303 (2015)

    Article  MathSciNet  Google Scholar 

  19. Blind, R., Allgower, F.: Analysis of Networked Event Based Control with a Shared Communication Medium: Part II in \(18^{th}\). IFAC World Congress, Milano, Italy (2011)

    Google Scholar 

  20. Bezzaoucha Rebaï, S., Voos, H.: Stability analysis of power networks under cyber-physical attacks: an LPV descriptor approach. In: \(6^{th}\) International Conference on Control, Decision and Information Technologies, Paris, France (2019)

  21. Ramesh, C., Sandberg, H., Bao, L., Johanson, K.: On the dual effect in state-based scheduling of networked control SYSTEMS in American Control Conference. California, San Francisco (2011)

    Google Scholar 

  22. Ge, H., Yue, D., Xie, X., et al.: Security control of networked T-S fuzzy system under intermittent DoS jamming attack with event-based predictor. Int. J. Fuzzy Syst. 21, 700–714 (2019). https://doi.org/10.1007/s40815-018-0593-1

    Article  MathSciNet  Google Scholar 

  23. Sun, W., Lv, X.: Practical finite-time fuzzy control for Hamiltonian systems via adaptive event-triggered approach. Int. J. Fuzzy Syst. 22, 35–45 (2020). https://doi.org/10.1007/s40815-019-00773-0

    Article  Google Scholar 

  24. Gao, C., Zhou, X., Liu, X., et al.: Observer-based adaptive fuzzy tracking control for a class of strict-feedback systems with event-triggered strategy and tan-type barrier Lyapunov function. Int. J. Fuzzy Syst. 22, 2534–2545 (2020). https://doi.org/10.1007/s40815-020-00948-0

    Article  Google Scholar 

  25. Bezzaoucha Rebaï, S., Voos, H., Darouach, M.: Attack tolerant control and observer-based trajectory tracking for cyber-physical systems. Eur. J. Control. (2018). https://doi.org/10.1016/j.ejcon.2018.09.005

    Article  MATH  Google Scholar 

  26. Bezzaoucha, S., Marx, B., Maquin, D., Ragot, J.: Contribution to the Constrained Output Feedback Control in American Control Conference. DC, USA, Washington (2013)

  27. Heemels, W., Johansson, K., Tabuada, P.: Event-Triggered and Self-Triggered Control. Springer-Encyclopedia of Systems and Control, 384–391 (2015). https://doi.org/10.1007/978-1-4471-5058-9-97.

  28. Tabuada, P.: Event-Triggered real time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52, 1680–1685 (2007)

    Article  MathSciNet  Google Scholar 

  29. Tarbouriech, S., Seuret, A., da Silva Jr, J.M.C., Sbarbaro, D.: Observer-based event-triggered control co-design for linear system. IET Control Theory Appl. 10, 2466–2473 (2016)

  30. Davoodi, M., Meskin, N., Khorasani, K.: Event triggered robust H1 control for linear systems. IEEE Trans. Ind. Inf. 13, 298–311 (2017)

    Article  Google Scholar 

  31. Zhou, K., Khargonekar, P.: Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Syst. Control Lett. 10, 17–20 (1988)

    Article  MathSciNet  Google Scholar 

  32. Bezzaoucha, S., Marx, B., Maquin, D., Ragot, J.: State and multiplicative sensor fault estimation for nonlinear systems. In: \(2^{nd}\) International Conference on Control and Fault-Tolerant Systems, Nice, France (2013)

  33. Bezzaoucha, S., Marx, B., Maquin, D., Ragot, J.: State and output feedback control for Takagi-Sugeno systems with saturated actuators. Int. J. Adapt. Control Signal Process. 30 (2016)

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Correspondence to Souad Bezzaoucha Rebai.

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Bezzaoucha Rebai, S. A Cyber-Security Contribution to Estimation and Event-Based Control Scheduling Co-design for Polytopic and T-S Fuzzy Models Using a Lyapunov Approach. Int. J. Fuzzy Syst. 24, 2662–2672 (2022). https://doi.org/10.1007/s40815-022-01282-3

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