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.
Similar content being viewed by others
References
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)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)
Tanaka, K., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Ed Hardcover. Wiley, New York (2001)
Sugeno, M., Kang, G.: Structure identification of fuzzy model. Fuzzy Sets Syst 15–33 (1988)
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)
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)
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
Angelis, G.Z.: System analysis, modelling and control with polytopic linear models, PhD thesis. Eindhoven Technische Universiteit, Eindhoven (2001)
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)
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)
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)
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)
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)
Murray-Smith, R., Johansen, T.: Multiple Model Approaches to Modelling and Control. Taylor and Francis, Milton Park (1997)
Sontag, E.: Mathematical Control Theory. Text in Applied Mathematics. Springer, New York (1998)
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)
Cervin, A., Henningsson: scheduling of event-triggered controllers on a shared NETWORK in 47th IEEE Conference Decision and Control CDC, Cancun, Mexico (2008)
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)
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)
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)
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)
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
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
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
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
Bezzaoucha, S., Marx, B., Maquin, D., Ragot, J.: Contribution to the Constrained Output Feedback Control in American Control Conference. DC, USA, Washington (2013)
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.
Tabuada, P.: Event-Triggered real time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52, 1680–1685 (2007)
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)
Davoodi, M., Meskin, N., Khorasani, K.: Event triggered robust H1 control for linear systems. IEEE Trans. Ind. Inf. 13, 298–311 (2017)
Zhou, K., Khargonekar, P.: Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Syst. Control Lett. 10, 17–20 (1988)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares no conflict of interest.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-022-01282-3