A Switching Control Approach for Uncertain Vehicle Suspension Systems with Actuator Failure


This paper investigates the switching control issue for uncertain vehicle suspension systems, meanwhile, actuator failure is taken into account. Takagi-Sugeno (T-S) fuzzy model is utilized to describe the considered uncertain suspension systems. Consider that most existing analysis results related to suspension systems are independent of membership functions, which may cause conservatism, thus, a novel membership functions-dependent Lyapunov function is employed in the stability analysis. In the proposed analysis technique, both of the information of membership functions and their derivatives are applied to reduce the conservativeness. A switching control strategy is proposed to assure that suspension constraint requirements are satisfied by using the information of time-derivative of membership. Lastly, a simulation example is shown to identify the availability of the approach put forward in this paper.

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  1. 1.

    Na, J., Huang, Y., Wu, X., Su, S., Li, G.: Adaptive finite-time fuzzy control of nonlinear active suspension systems with input delay. IEEE Trans. Cybern. 50(6), 2639–2650 (2019)

    Article  Google Scholar 

  2. 2.

    Fei, Z., Wang, X., Liu, M., Yu, J.: Reliable control for vehicle active suspension systems under event-triggered scheme with frequency range limitation. IEEE Trans. Syst. Man Cybern. (2019). https://doi.org/10.1109/TSMC.2019.2899942

    Article  Google Scholar 

  3. 3.

    Na, J., Huang, Y., Pei, Q., Wu, X., Gao, G., Li, G.: Active suspension control of full-car systems without function approximation. IEEE/ASME Trans. Mech. 25(2), 779–791 (2020)

    Article  Google Scholar 

  4. 4.

    Gao, H., Sun, W., Shi, P.: Robust Sampled-Data \({H}_{\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 18(1), 238–245 (2009)

    Article  Google Scholar 

  5. 5.

    Sun, W., Gao, H., Kaynak, O.: Finite frequency \({H}_{\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2010)

    Article  Google Scholar 

  6. 6.

    Li, H., Jing, X., Karimi, H.R.: Output-feedback-based \({H}_{\infty }\) control for vehicle suspension systems with control delay. IEEE Trans. Ind. Elect. 61(1), 436–446 (2013)

    Article  Google Scholar 

  7. 7.

    Zhang, Z., Zhou, Q., Wu, C., Li, H.: Dissipativity-based reliable interval type-2 fuzzy filter design for uncertain nonlinear systems. Int. J. Fuzzy Syst. 20(2), 390–402 (2018)

    MathSciNet  Article  Google Scholar 

  8. 8.

    Li, W., Xie, Z., Zhao, J., Chu, S., Wong, P.K., Gao, J.: Improved adaptive event-triggered robust control for networked T-S fuzzy systems with asynchronous constraints. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2989404

    Article  Google Scholar 

  9. 9.

    Li, W., Xie, Z., Wong, P.K., Mei, X., Zhao, J.: Adaptive-event-triggered-based fuzzy nonlinear lateral dynamic control for autonomous electric vehicles under insecure communication networks. IEEE Trans. Ind. Elect. (2020). https://doi.org/10.1109/TIE.2020.2970680

    Article  Google Scholar 

  10. 10.

    Pan, Y., Du, P., Xue, H., Lam, H.K.: Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2999746

    Article  Google Scholar 

  11. 11.

    Zhu, Z., Pan, Y., Zhou, Q., Lu, C.: Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2973950

    Article  Google Scholar 

  12. 12.

    Du, P., Pan, Y., Li, H., Lam, H.K.: Nonsingular finite-time event-triggered fuzzy control for large-scale nonlinear systems. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2992632

    Article  Google Scholar 

  13. 13.

    Xiao, W., Cao, L., Li, H., Lu, R.: Observer-based adaptive consensus control for nonlinear multi-agent systems with time-delay. Sci. China Inf. Sci. 63(3), 132202 (2020)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Du, P., Sun, K., Zhao, S., Liang, H.: Observer-based adaptive fuzzy control for time-varying state constrained strict-feedback nonlinear systems with dead-zone. Int. J. Fuzzy Syst. 21(3), 733–744 (2019)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Li, Q., Pan, Y., Zhang, Z., Lam, H.K.: Reliable dissipative interval type-2 fuzzy control for nonlinear systems with stochastic incomplete communication route and actuator failure. Int. J. Fuzzy Syst. 22(2), 368–379 (2020)

    MathSciNet  Article  Google Scholar 

  16. 16.

    Tong, S., Min, X., Li, Y.: Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2977175

    Article  Google Scholar 

  17. 17.

    Liang, Y., Li, Y., Che, W., Hou, Z.: Adaptive fuzzy asymptotic tracking for nonlinear systems with nonstrict feedback structure. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3002242

    Article  Google Scholar 

  18. 18.

    Hua, C., Li, Y., Guan, X.: Finite/fixed-time stabilization for nonlinear interconnected systems with dead-zone input. IEEE Trans. Autom. Control 62(5), 2554–2560 (2017)

    MathSciNet  Article  Google Scholar 

  19. 19.

    Yao, D., Li, H., Lu, R., Shi, Y.: Distributed sliding mode tracking control of second-order nonlinear multi agent systems: An event-triggered approach. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2963087

    Article  Google Scholar 

  20. 20.

    Pan, Y., Yang, G.: Event-triggered fuzzy control for nonlinear networked control systems. Fuzzy Sets Syst. 329(15), 91–107 (2017)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Ma, H., Li, H., Lu, R., Huang, T.: Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances. Sci. China Inf. Sci. 63(5), 1502121–15021215 (2020)

    MathSciNet  Article  Google Scholar 

  22. 22.

    Wang, Y., Shen, H., Karimi, H.R., Duan, D.: Dissipativity-based fuzzy integral sliding mode control of continuous-time T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 26(3), 1164–1176 (2017)

    Article  Google Scholar 

  23. 23.

    Zhang, D., Wang, Q., Yu, L.: Distributed non-fragile filtering for T-S fuzzy systems with event-based communications. Fuzzy Sets Syst. 306, 137–152 (2017)

    MathSciNet  Article  Google Scholar 

  24. 24.

    Zhang, C., Hu, J., Qiu, J., Chen, Q.: Reliable output feedback control for T-S fuzzy systems with decentralized event triggering communication and actuator failures. IEEE Trans. Cybern. 47(9), 2592–2602 (2017)

    Article  Google Scholar 

  25. 25.

    Li, H., Jing, X., Lam, H.K., Shi, P.: Fuzzy sampled-data control for uncertain vehicle suspension systems. IEEE Trans. Cybern. 44(7), 1111–1126 (2013)

    Google Scholar 

  26. 26.

    Sun, S., Tang, X., Yang, J., Ning, D., Du, H., Zhang, S., Li, W.: A new generation of magnetorheological vehicle suspension system with tunable stiffness and damping characteristics. IEEE Trans. Ind. Inf. 15(8), 4696–4708 (2019)

    Article  Google Scholar 

  27. 27.

    Tang, X., Du, H., Sun, S., Ning, D., Xing, Z., Li, W.: Takagi-Sugeno fuzzy control for semi-active vehicle suspension with a magnetorheological damper and experimental validation. IEEE/ASME Trans. Mech. 22(1), 291–300 (2016)

    Article  Google Scholar 

  28. 28.

    Guan, X., Chen, C.: Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays. IEEE Trans. Fuzzy Syst. 12(2), 236–249 (2004)

    Article  Google Scholar 

  29. 29.

    Wang, L., Lam, H.K.: A new approach to stability and stabilization analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 26(4), 2460–2465 (2017)

    Article  Google Scholar 

  30. 30.

    Li, H., Liu, H., Gao, H., Shi, P.: Reliable fuzzy control for active suspension systems with actuator delay and fault. IEEE Trans. Fuzzy Syst. 20(2), 342–357 (2011)

    Article  Google Scholar 

  31. 31.

    Liu, B., Saif, M., Fan, H.: Adaptive fault tolerant control of a half-car active suspension systems subject to random actuator failures. IEEE/ASME Trans. Mech. 21(6), 2847–2857 (2016)

    Article  Google Scholar 

  32. 32.

    Mao, Z., Wang, Y., Jiang, B., Tao, G.: Fault diagnosis for a class of active suspension systems with dynamic actuators’ faults. Int. J. Control Autom. Syst. 14(5), 1160–1172 (2016)

    Article  Google Scholar 

  33. 33.

    Mrazgua, J., Ouahi, M.: Fuzzy fault-tolerant \({H}_{\infty }\) control approach for nonlinear active suspension systems with actuator failure. Proc. Computer Sci. 148, 465–474 (2019)

    Article  Google Scholar 

  34. 34.

    Li, H., Zhang, Z., Yan, H., Xie, X.: Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern. 49(12), 4388–4397 (2018)

    Article  Google Scholar 

  35. 35.

    Li, S., Ahn, C.K., Xiang, Z.: Command filter based adaptive fuzzy finite-time control for switched nonlinear systems using state-dependent switching method. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2965917

    Article  Google Scholar 

  36. 36.

    Li, S., Ahn, C.K., Xiang, Z.: Adaptive fuzzy control of switched nonlinear time-varying delay systems with prescribed performance and unmodeled dynamics. Fuzzy Sets Syst. 371, 40–60 (2019)

    MathSciNet  Article  Google Scholar 

  37. 37.

    Liang, H., Zhang, Z., Ahn, C.K.: Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circ. Syst. 67(2), 335–339 (2020)

    Google Scholar 

  38. 38.

    Zhang, Z., Liang, H., Wu, C., Ahn, C.K.: Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and actuator failure. IEEE Trans. Fuzzy Syst. 27(9), 1793–1806 (2019)

    Article  Google Scholar 

  39. 39.

    Liu, Y., Liu, X., Jing, Y., Li, X.: Annular domain finite-time connective control for large-scale systems with expanding construction. IEEE Trans. Syst. Man Cybern. (2019). https://doi.org/10.1109/TSMC.2019.2960009

    Article  Google Scholar 

  40. 40.

    Zhou, Q., Chen, G., Lu, R., Bai, W.: Disturbance-observer-based event-triggered control for multi-agent systems with input saturation. Sci. Sin. Inform. 49(11), 1502–1516 (2019)

    Article  Google Scholar 

  41. 41.

    Yang, D., Li, X., Qiu, J.: Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback. Nonlinear Anal. 32, 294–305 (2019)

    MathSciNet  MATH  Google Scholar 

  42. 42.

    Liang, H., Guo, X., Pan, Y., Huang, T.: Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2982618

    Article  Google Scholar 

  43. 43.

    Li, X., Yang, X., Huang, T.: Persistence of delayed cooperative models: impulsive control method. Appl. Math. Comput. 342, 130–146 (2019)

    MathSciNet  MATH  Google Scholar 

  44. 44.

    Liang, Z., Zhao, J., Dong, Z., Wang, Y., Ding, Z.: Torque vectoring and rear-wheel-steering control for vehicle’s uncertain slips on soft and slope terrain using sliding mode algorithm. IEEE Trans. Vehicular Technol. 69(4), 3805–3815 (2020)

    Article  Google Scholar 

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This work was partially supported by the PhD Start-up Fund of Liaoning Province (2020-BS-239).

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Correspondence to Yingnan Pan.

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Li, Q., Pan, Y. & Liang, H. A Switching Control Approach for Uncertain Vehicle Suspension Systems with Actuator Failure. Int. J. Fuzzy Syst. (2021). https://doi.org/10.1007/s40815-020-00961-3

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  • Uncertain suspension systems
  • Actuator failure
  • Switching fuzzy controller
  • Membership functions-dependent Lyapunov function