DOI QR코드

DOI QR Code

Event-Triggered Model Predictive Control for Continuous T-S fuzzy Systems with Input Quantization

양자화 입력을 고려한 연속시간 T-S 퍼지 시스템을 위한 이벤트 트리거 모델예측제어

  • Kwon, Wookyong (Graduate Institute of Ferrous Technology (GIFT), POSTECH) ;
  • Lee, Sangmoon (Dept. of Electronic Engineering, Kyungpook National University)
  • Received : 2017.07.17
  • Accepted : 2017.07.31
  • Published : 2017.09.01

Abstract

In this paper, a problem of event-triggered model predictive control is investigated for continuous-time Takagi-Sugeno (T-S) fuzzy systems with input quantization. To efficiently utilize network resources, event-trigger is employed, which transmits limited signals satisfying the condition that the measurement of errors is over the ratio of a certain level. Considering sampling and quantization, continuous Takagi-Sugeno (T-S) fuzzy systems are regarded as a sector bounded continuous-time T-S fuzzy systems with input delay. Then, a model predictive controller (MPC) based on parallel distributed compensation (PDC) is designed to optimally stabilize the closed loop systems. The proposed MPC optimize the objective function over infinite horizon, which can be easily calculated and implemented solving linear matrix inequalities (LMIs) for every event-triggered time. The validity and effectiveness are shown that the event triggered MPC can stabilize well the systems with even smaller average sampling rate and limited actuator signal guaranteeing optimal performances through the numerical example.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. H. O. Wanag, K. Tanaka, M.F. Griffin, "An approach to fuzzy control of nonlinear systems: stability and design issues", IEEE Trans. Fuzzy Syst..vol. 4, no. 1, pp. 14-23, 1996. https://doi.org/10.1109/91.481841
  2. T. M. Guerra, L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in takagi-sugeno's form", Automatica, vol. 40, no. 5, pp. 823-829, 2004. https://doi.org/10.1016/j.automatica.2003.12.014
  3. K. Tanaka, T. Hori, H.O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems", IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 582-589, 2003. https://doi.org/10.1109/TFUZZ.2003.814861
  4. C.H. Fang, Y.S. Liu, S.W. Kau, L. Hong, C.H. Lee, "A new LMI-based approach to relaxed quadratic stabilization of ts fuzzy control systems", IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 486-397, 2006.
  5. X. Zhao, L. Zhang, P. Shi, and H. R. Karimi, "Novel stability criteria for T-S fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 22, no. 2, pp. 313-323, 2014. https://doi.org/10.1109/TFUZZ.2013.2254491
  6. S. Tong and H.X. Li, "Fuzzy adaptive sliding-mode control for MIMO nonlinear systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 3, pp. 354-360, 2003. https://doi.org/10.1109/TFUZZ.2003.812694
  7. K. Tanaka, H. Ohtake, H.O. Wang, "Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach", IEEE Trans. Syst. Man Cybernet. Part B: Cybernet., vol. 39, no. 2, pp. 561-567, 2009. https://doi.org/10.1109/TSMCB.2008.2006639
  8. S. Hu, D. Yue, "Event-triggered control design of linear networked systems with quantizations,", ISA Trans., vol. 51, no. 1, pp. 153-162, 2012. https://doi.org/10.1016/j.isatra.2011.09.002
  9. X. Wang, M.D. Lemmon. "Event-triggering in distributed networked control systems", IEEE Trans. Automat. Control, vol. 56, no. 3, pp. 586-501, 2011. https://doi.org/10.1109/TAC.2010.2057951
  10. C. Peng, Q.L. Han, "A novel event-triggered transmission scheme and control co-design for sampled-data control systems", IEEE Trans. Automat. Control, vol. 58, no. 10, pp. 2620-2626, 2013. https://doi.org/10.1109/TAC.2013.2256015
  11. K. Zhang, M. Zheng, Y. Zhang, "Control strategies for network systems based on a novel event-trigger mechanism", Asian Simulation Conference, pp. 120-126, 2016.
  12. C. Peng, Q.L. Han, D. Yue, "To transmit or not to transmit: a discrete event-triggered communication scheme for networked takagi-sugeno fuzzy systems", IEEE Trans. Fuzzy Syst., vol. 21, no. 1, pp. 164-170, 2013. https://doi.org/10.1109/TFUZZ.2012.2199994
  13. J. Qiu, H. Gao, S.X. Ding, "Recent advances on fuzzy-model-based nonlinear networked control systems: a survey", IEEE Trans. Industrial Electronis, vol. 63, no. 2, pp. 1207-1217, 2016. https://doi.org/10.1109/TIE.2015.2504351
  14. D. Yue, E. Tian, Y. Zhang, C. Peng, "Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay", IEEE Trans. Syst. Man Cybernet. Part B: Cybernet., vol. 39, no. 2, pp. 503-516, 2009. https://doi.org/10.1109/TSMCB.2008.2007496
  15. A. Seuret, F. Gouaisbaut, "Wirtinger-based integral inequality: application to time-delay systems", Automatica, vol. 49, no. 9, pp. 2860-2866, 2013. https://doi.org/10.1016/j.automatica.2013.05.030
  16. H.D. Tuan, P. Apkarian, T. Narikiyo, Y. Yamamoto, "Parameterized linear matrix inequality techniques in fuzzy control system design", IEEE Trans. Fuzzy Syst., vol. 9, no. 2, pp. 324-332, 2001. https://doi.org/10.1109/91.919253
  17. E. Fridman, M. Dambrine, "Control under quantization, saturation and delay: An LMI approach", Automatica, vol. 45, no. 10, pp. 2258-2264, 2009. https://doi.org/10.1016/j.automatica.2009.05.020