Abstract
The present work investigates the Takagi–Sugeno (T–S) fuzzy-based fault-tolerant control for non-linear descriptor systems with uncertainties, external disturbances, and actuator failures. More precisely, the sliding mode control (SMC) approach is employed to develop an observer-based (SMC) strategy for this class of models with the assumption that the sub-model-input matrices can be different. First, an observer is designed to reconstruct the unmeasured states, and a novel integral sliding function, which involves a non-linear term to compensate the matched uncertainty, is formulated. Based on an appropriate fuzzy Lyapunov function, sufficient conditions are established in terms of linear matrix inequality (LMI) to ensure the robust admissibility of the closed-loop system with a satisfactory mixed \(H_\infty \) /passivity performance and determine the sliding function parameters. Then, an adaptive observer-based SMC law is synthesized to adaptively ensure the reachability of the sliding surface and completely compensate for the influence of the previously mentioned factors. Finally, the efficiency of the theoretical findings is shown by the implementation of the proposed reliable SMC controller for practical systems about the pendulum and truck-trailer.
Similar content being viewed by others
Abbreviations
- TSFS:
-
Takagi–Sugeno fuzzy systems
- FTCS:
-
Fault tolerant control systems
- CLS:
-
Closed loop system
- SMC:
-
Sliding mode control
- PLMI:
-
Parametrized linear matrix inequality
References
Alwi, H., Edwards, C.: Fault tolerant control using sliding modes with on-line control allocation. Automatica 44, 1859–1866 (2008)
Castaños, F., Hernández, D., Fridman, L.M.: Integral sliding-mode control for linear time-invariant implicit systems. Automatica 50(3), 971–975 (2014)
Chang, J.: Dynamic output feedback integral sliding mode control design for uncertain systems. Int. J. Robust Nonlinear Control 12, 841–857 (2012)
Chen, J., Lin, C., Chen, B., Wang, Q.: Mixed \(H_\infty \) and passive control for singular systems with time delay via static output feedback. Appl. Math. Comput. 293, 244–253 (2017)
Cunha, J., Costa, R., Hsu, L., Oliveira, T.: Output-feedback sliding-mode control for systems subjected to actuator and internal dynamics failures. IET Control Theory Appl. 9, 637–647 (2015)
Dai, L.: Singular Control Systems. Lecture Notes in Control and Information Sciences, vol. 118. Springer, New York (1989)
Gassara, H., El Hajjaji, A., Kchaou, M., Chaabane, M.: Observer based (Q, V, R)-\( \alpha \)-dissipative control for TS fuzzy descriptor systems with time delay. J. Franklin Inst. 351(1), 187–206 (2014)
Hamidi, F., Jerbi, H.: On the estimation of a maximal lyapunov function and domain of attraction determination via a genetic algorithm. In: 2009 6th International Multi-Conference on Systems, Signals and Devices, pp. 1–6. Tunisia (2009)
Han, Y., Kao, Y., Gao, C.: Robust observer-based \(H_\infty \) control for uncertain discrete singular systems with time-varying delays via sliding mode approach. ISA Trans. 80, 81–88 (2018)
Han, Y., Kao, Y., Park, J.: Robust H\(_\infty \) non-fragile observer-based control of switched discrete singular systems with time-varying delays: a sliding mode control design. Int. J. Robust Nonlinear Control 29, 1462–1483 (2019)
Hernández, D., Fridman, L., Golkani, M.: Continuous sliding-mode control for singular systems. Int. J. Robust Nonlinear Control 28, 3454–3474 (2018)
Jiang, B., Gao, C., Xie, J.: Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations. Appl. Math. Comput. 271, 187–200 (2015)
Jiang, B., Kao, Y., Gao, C., Yao, X.: Passification of uncertain singular semi-Markovian jump systems with actuator failures via sliding mode approach. IEEE Trans. Autom. Control 62, 4138–4143 (2017)
Jiang, B., Karimi, H.R., Kao, Y., Gao, C.: A novel robust fuzzy integral sliding mode control for nonlinear semi-Markovian jump t–s fuzzy systems. IEEE Trans. Fuzzy Syst. 26(6), 3594–3604 (2018). https://doi.org/10.1109/TFUZZ.2018.2838552
Kchaou, M.: Robust observer-based sliding mode control for nonlinear uncertain singular systems with time-varying delay and input non-linearity. Eur. J. Control 49, 15–25 (2019)
Kchaou, M., El-Hajjaji, A.: Resilient \(H_\infty \) sliding mode control for discrete-time descriptor fuzzy systems with multiple time delays. Int. J. Syst. Sci. 48, 288–3014 (2017)
Kchaou, M., Gassara, H., El-Hajjaji, A.: Adaptive sliding mode control for fuzzy singular systems with time delay and input nonlinearity. Int. J. Adapt. Control Signal Process. 3(32), 464–479 (2018)
Kchaou, M., Mahmoud, M.: Robust \((Q, S, R)-\gamma \)-dissipative sliding mode control for uncertain discrete-time descriptor systems with time-varying delay. IMA J. Math. Control Inf. 32, 1–22 (2017)
Khooban, M.H., Niknam, T., Blaabjerg, F., Dehghani, M.: Free chattering hybrid sliding mode control for a class of non-linear systems: electric vehicles as a case study. IET Sci. Meas. Technol. 10, 776–785 (2016)
Lai, G., Liu, Z., Chen, C.P., Zhang, Y., Chen, X.: Adaptive compensation for infinite number of time-varying actuator failures in fuzzy tracking control of uncertain non-linear systems. IEEE Trans. Fuzzy Syst. 2, 474–486 (2018)
Li, F., Shi, P., Wu, L., Zhang, X.: Fuzzy-model-based D-stability and non-fragile control for discrete-time descriptor systems with multiple delays. IEEE Trans. Fuzzy Syst. 22(4), 1019–1025 (2014)
Li, H., Shi, P., Yao, D., Wu, L.: Observer-based adaptive sliding mode control for nonlinear Markovian jump systems. Automatica 64, 133–142 (2016)
Li, J., Yang, G.H.: Fuzzy descriptor sliding mode observer design: a canonical form-based method. IEEE Trans. Fuzzy Syst. 28(9), 2048–2062 (2020)
Li, J., Zhang, Q.: An integral sliding mode control approach to observer-based stabilization of stochastic Itô descriptor systems. Neurocomputing 173, 1330–1340 (2016)
Li, J., Zhang, Q., Yan, X., Spurgeon, S.K.: Integral sliding mode control for Markovian jump TS fuzzy descriptor systems based on the super-twisting algorithm. IET Control Theory Appl. 11(8), 1134–1143 (2017). https://doi.org/10.1049/iet-cta.2016.0862
Li, J., Zhang, Q., Yan, X., Spurgeon, S.: Robust stabilization of TS fuzzy stochastic descriptor systems via integral sliding modes. IEEE Trans. Cybern. 48, 4736–4749 (2017)
Li, J., Zhang, Q., Yan, X., Spurgeon, S.K.: Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems. IEEE Trans. Fuzzy Syst. 26(5), 2818–2832 (2018). https://doi.org/10.1109/TFUZZ.2018.2802458
Li, R., Zhang, Q.: Robust \(H_\infty \) sliding mode observer design for a class of Takagi-Sugeno fuzzy descriptor systems with time-varying delay. Appl. Math. Comput. 337, 158–178 (2018)
Li, W., Feng, Z., Sun, W., Zhang, J.: Admissibility analysis for Takagi-Sugeno fuzzy singular systems with time delay. Neurocomputing 205, 336–340 (2016)
Li, X., Shen, X.: A data-driven attack detection approach for dc servo motor systems based on mixed optimization strategy. IEEE Trans. Ind. Inf. 16(9), 5806–5813 (2020)
Li, X., Yang, G.: Fault detection in finite frequency domain for Takagi–Sugeno fuzzy systems with sensor faults. IEEE Trans. Cybernet. 44(8), 1446–1458 (2014)
Liu, Y., Niu, Y., Lam, J., Zhang, B.: Sliding mode control for uncertain switched systems with partial actuator faults. Asian J. Control 1(5), 1–10 (2014)
Liu, Z., Zhao, L., Gao, C.: Observer-based adaptive \( {H}_{\infty }\) control of uncertain stochastic singular systems via integral sliding mode technique. IET Control Theory Appl. 11(5), 668–676 (2017). https://doi.org/10.1049/iet-cta.2016.0911
Liu, Z., Zhao, L., Xiao, H., Gao, C.: Adaptive \( {H}_{\infty }\) integral sliding mode control for uncertain singular time-delay systems based on observer. Circ. Syst. Signal Process. 36(11), 4365–4387 (2017)
Ma, Y., Yang, P., Zhang, Q.: Robust H\(_\infty \) control for uncertain singular discrete T-S fuzzy time-delay systems with actuator saturation. J. Franklin Inst. 13(353), 3290–3311 (2016)
Niu, Y., Liu, Y., Jia, T.: Reliable control of stochastic systems via sliding mode technique. Optim. Control Appl. Meth 34, 712–727 (2013)
Petersen, I.: A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8, 35–357 (1987)
Regaieg, M., Bosche, J., Kchaou, M., Hajjaji, A., Chaabane, M.: DU-admissibility with static output feedback for uncertain descriptor TS systems. Int. J. Syst. Sci. 50(10), 2030–2041 (2019)
Su, Z., Zhang, Q., Ai, J., Sun, X.: Finite-time fuzzy stabilisation and control for nonlinear descriptor systems with non-zero initial state. Int. J. Syst. Sci. 46(2), 364–376 (2015)
Tuan, H., Apkarian, P., Narikiyo, T., Yamamoto, Y.: Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Trans. Fuzzy Syst. 9(2), 324–332 (2001)
Wang, Y., Fei, J.: Adaptive sliding mode control for PMSM position regulation system. Int. J. Innov. Comput. Inf. Control 11(3), 881–891 (2015)
Wang, Y., Karimi, H., Shen, H., Fang, Z., Liu, M.: Fuzzy-model-based sliding mode control of nonlinear descriptor systems. IEEE Trans. Cybernet. 49–9, 3409–3419 (2019). https://doi.org/10.1109/TCYB.2018.2842920
Wu, G.: Reliable passivity and passification for singular Markovian systems. IMA J. Math. Control Inf. 20, 155–168 (2013)
Wu, L., Zheng, W.: Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica 45, 2120–2127 (2009)
Wu, Z., Li, B., Gao, C., Jiang, B.: Observer-based H\(_\infty \) control design for singular switching semi-Markovian jump systems with random sensor delays. ISA Trans. (2019). https://doi.org/10.1016/j.isatra.2019.09.002
Xu, S., Liu, Y.: Study of Takagi–Sugeno fuzzy-based terminal-sliding mode fault-tolerant control. IET Control Theory Appl. 8, 667–674 (2014)
Yang, P., Ma, Y., Yang, F., Kong, D., Wang, L.: Passivity control for uncertain singular discrete TS fuzzy time-delay systems subject to actuator saturation. Int. J. Syst. Sci. 49–8, 1627–1640 (2018). https://doi.org/10.1080/00207721.2018.1464608
Zeng, Y., Han, C., Na, Y., Lu, Z.: Fuzzy-model-based admissibility analysis for nonlinear discrete-time descriptor system with time-delay. Neurocomputing 189, 80–85 (2016)
Zhang, L., Wu, J.: Reliable control for time-varying delay switched fuzzy systems with faulty actuators based on observers switching method. Math. Problems Eng. 2013, 1–12 (2013)
Zhang, Q., Li, R., Ren, J.: Robust adaptive sliding mode observer design for T–S fuzzy descriptor systems with time-varying delay. IEEE Access 6, 46002–46017 (2018)
Zhang, Y., Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control systems. Annu. Rev. Control 32, 229–252 (2008)
Zheng, Q., Ling, Y., Wei, L., Zhang, H.: Mixed \(H_\infty \) and passive control for linear switched systems via hybrid control approach. Int. J. Syst. Sci. 49, 818–832 (2018). https://doi.org/10.1080/00207721.2018.1424967
Acknowledgements
The authors express their gratitude to the research deanship of Hail University in KSA for their financial support and sponsorship in their pledge for this research (funding scheme (RG-0191315)).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kchaou, M., Jerbi, H. Reliable H∞ and Passive Fuzzy Observer-Based Sliding Mode Control for Nonlinear Descriptor Systems Subject to Actuator Failure. Int. J. Fuzzy Syst. 24, 105–120 (2022). https://doi.org/10.1007/s40815-021-01121-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-021-01121-x