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Robust Observer-Based Fuzzy Control Via Proportional Derivative Feedback Method for Singular Takagi–Sugeno Fuzzy Systems

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Abstract

This paper investigates a robust observer-based control problem for uncertain nonlinear singular systems. Based on the modeling approach, the system is described by Takagi–Sugeno (T–S) fuzzy model such that the linear theories can be applied to discuss the problem. To guarantee the regularity and impulse-free property, proportional derivative (PD) control scheme and parallel distributed compensation (PDC) concept are employed to construct the fuzzy controller. Furthermore, a PD fuzzy observer is also designed to ensure the existence the derivative term of controller and to estimate the unmeasurable states. For the problem, a Lyapunov function and converting technologies are applied to derive less conservative stability criterion. Moreover, some sufficient conditions are transferred into Linear Matrix Inequality (LMI) form for using convex optimization algorithm. In addition, uncertainty is also considered for practical operation to achieve robustness of the closed loop system. According to the uncertainty and the derived conditions, a general and relaxed observer-based fuzzy controller design method is proposed to guarantee the robust asymptotical stability of the uncertain nonlinear singular systems. Finally, two numerical examples are provided to verify the applicability and availability of the proposed design method.

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References

  1. Tian, Y., Wang, Z.: Finite-time extended dissipative filtering for singular T-S fuzzy systems with nonhomogeneous Markov jumps. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3030503

    Article  Google Scholar 

  2. Li, L., Zhang, Q., Zhu, B.: Fuzzy stochastic optimal guaranteed cost control of bio-economic singular Markovian jump systems. IEEE Trans. Cybern. 45(11), 2512–2521 (2015)

    Article  Google Scholar 

  3. Sakthivel, R., Kanagaraj, R., Wang, C., Selvaraj, P., Anthoni, S.M.: Non-fragile sampled-data guaranteed cost control for bio-economic fuzzy singular Markovian jump systems. IET Control Theory Appl. 13(2), 279–287 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Qi, W., Zong, G., Karim, H.R.: Observer-based adaptive SMC for nonlinear uncertain singular semi-Markov jump systems with applications to DC motor. IEEE Trans. Circuits Syst. I Regul. Pap. 65(9), 2951–2960 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  5. Verghese, G., Lévy, B., Kailath, T.: A generalized state-space for singular systems. IEEE Trans. Autom. Control 26(4), 811–831 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dai, L.: Singular control systems. Springer, Berlin (1989)

    Book  MATH  Google Scholar 

  7. Zheng, Q., Ling, Y., Wei, L., Zhang, H.: Mixed and passive control for linear switched systems via hybrid control approach. Int. J. Syst. Sci. 49(4), 818–832 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhong, R., Yang, Z.: Delay-dependent robust control of descriptor systems with time delay. Asian J. Control 8(1), 36–44 (2006)

    Article  MathSciNet  Google Scholar 

  9. Zhang, X., Chen, Y.: Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order: the case. ISA Trans. 82, 42–50 (2018)

    Article  Google Scholar 

  10. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. (1985). https://doi.org/10.1109/TSMC.1985.6313399

    Article  MATH  Google Scholar 

  11. Chang, C.M., Chang, W.J.: Robust fuzzy control with transient and steady-state performance constraints for ship fin stabilizing systems. Int. J. Fuzzy Syst. 21(2), 518–531 (2019)

    Article  MathSciNet  Google Scholar 

  12. Chen, J., Yu, J.: Robust control for discrete-time T-S fuzzy singular systems. J. Syst. Sci. Complex. 34(4), 1345–1363 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pan, S., Ye, Z., Zhou, J.: robust control based on event-triggered sampling for hybrid systems with singular Markovian jump. Math. Methods Appl. Sci. 42(3), 790–805 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, H.O., Tanaka, K., Griffin, M.F.: An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans. Fuzzy Syst. 4(1), 14–23 (1996)

    Article  Google Scholar 

  15. Zhang, J., Liu, D., Ma, Y.: Finite-time dissipative control of uncertain singular T-S fuzzy time-varying delay systems subject to actuator saturation. Comput. Appl. Math. 39(3), 1–22 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wei, Z., Ma, Y.: Robust observer-based sliding mode control for uncertain Takagi-Sugeno fuzzy descriptor systems with unmeasurable premise variables and time-varying delay. Inf. Sci. 566, 239–261 (2021)

    Article  MathSciNet  Google Scholar 

  17. Wu, J.: Robust stabilization for uncertain T-S fuzzy singular system. Int. J. Mach. Learn. Cybern. 7(5), 699–706 (2016)

    Article  Google Scholar 

  18. Chang, W.J., Su, C.L., Varadarajan, V.: Fuzzy controller design for nonlinear singular systems with external noises subject to passivity constraints. Asian J. Control 23(3), 1195–1211 (2021)

    Article  MathSciNet  Google Scholar 

  19. Zhang, Q., Qiao, L., Zhu, B., Zhang, H.: Dissipativity analysis and synthesis for a class of T-S fuzzy descriptor systems. IEEE Trans. Syst. Man Cybern.: Syst. 47(8), 1774–1784 (2016)

    Article  Google Scholar 

  20. Chang, W.J., Su, C.L., Tsai, M.H.: Derivative-based fuzzy control synthesis for singular Takagi-Sugeno fuzzy systems with perturbations. In: Proceedings of international symposium on electrical, electronics and information engineering. (2021)

    Google Scholar 

  21. Mu, Y., Zhang, H., Su, H., Wang, Y.: Robust normalization and H∞ stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays. Appl. Math. Comput. 388, 125534 (2021)

    MathSciNet  MATH  Google Scholar 

  22. Li, R., Zhang, Q.: Robust sliding mode observer design for a class of Takagi-Sugeno fuzzy descriptor systems with time-varying delay. Appl. Math. Comput. 337, 158–178 (2018)

    MathSciNet  MATH  Google Scholar 

  23. Kchaou, M.: Robust observer-based control for a class of (TS) fuzzy descriptor systems with time-varying delay. Int. J. Fuzzy Syst. 19(3), 909–924 (2017)

    Article  MathSciNet  Google Scholar 

  24. Zhang, X., Jin, K.: State and output feedback controller design of Takagi-Sugeno fuzzy singular fractional order systems. Int. J. Control Autom. Syst. 19(6), 2260–2268 (2021)

    Article  Google Scholar 

  25. Wang, J., Ma, S., Zhang, C.: Finite-time control for T-S fuzzy descriptor semi-Markov jump systems via static output feedback. Fuzzy Sets Syst. 365, 60–80 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  26. Mu, Y., Zhang, H., Sun, S., Ren, J.: Robust non-fragile proportional plus derivative state feedback control for a class of uncertain Takagi-Sugeno fuzzy singular systems. J. Franklin Inst. 356(12), 6208–6225 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  27. Chang, W.J., Lian, K.Y., Su, C.L., Tsai, M.H.: Multi-constrained fuzzy control for perturbed T-S fuzzy singular systems by proportional-plus-derivative state feedback method. Int. J. Fuzzy Syst. 23(7), 1972–1985 (2021)

    Article  Google Scholar 

  28. Mu, Y., Zhang, H., Sun, J., Ren, J.: Proportional plus derivative state feedback controller design for a class of fuzzy descriptor systems. Int. J. Syst. Sci. 50(12), 2249–2260 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  29. Gao, Z., Liu, Y., Wang, Z.: On stabilization of linear switched singular systems via PD state feedback. IEEE Access 8, 97007–97015 (2020)

    Article  Google Scholar 

  30. Mu, Y., Tan, Z., Zhang, H., Zhang, J.: Proportional derivative observer design for nonlinear singular systems. In: Proceeding of IEEE 8th data driven control and learning systems conference, pp. 111–116. (2019)

    Google Scholar 

  31. Mu, Y., Zhang, H., Yan, Y., Wu, Z.: A design framework of nonlinear H∞ PD observer for one-sided Lipschitz singular systems with disturbances. IEEE Trans. Circuits Syst. II: Express Briefs (2022). https://doi.org/10.1109/TCSII.2022.3166677

    Article  Google Scholar 

  32. Ku, C.C., Chang, W.J., Tsai, M.H., Lee, Y.C.: Observer-based proportional derivative fuzzy control for singular Takagi-Sugeno fuzzy systems. Inf. Sci. 570, 815–830 (2021)

    Article  MathSciNet  Google Scholar 

  33. Chang, W.J., Tsai, M.H., Pen, C.L.: Observer-based fuzzy controller design for nonlinear discrete-time singular systems via proportional derivative feedback scheme. Appl. Sci. 11(6), 2833 (2021)

    Article  Google Scholar 

  34. Apkarian, P., Tuan, H.D., Bernussou, J.: Continuous-time analysis, eigenstructure assignment, and synthesis with enhanced linear matrix inequalities (LMI) characterizations. IEEE Trans. Autom. Control 46(12), 1941–1946 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  35. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

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Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers who gave us many constructive comments and suggestions. This work was supported by the Ministry of Science and Technology of the Republic of China under Contract MOST 110-2221-E-019-076.

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Authors and Affiliations

  1. Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, 806, Taiwan, ROC

    Cheung-Chieh Ku

  2. Department of Marine Engineering, National Taiwan Ocean University, Keelung, 202, Taiwan, ROC

    Wen-Jer Chang & Yu-Min Huang

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  1. Cheung-Chieh Ku
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Correspondence to Wen-Jer Chang.

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Ku, CC., Chang, WJ. & Huang, YM. Robust Observer-Based Fuzzy Control Via Proportional Derivative Feedback Method for Singular Takagi–Sugeno Fuzzy Systems. Int. J. Fuzzy Syst. 24, 3349–3365 (2022). https://doi.org/10.1007/s40815-022-01369-x

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  • DOI: https://doi.org/10.1007/s40815-022-01369-x

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