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Control of Takagi–Sugeno Fuzzy Fast/Slow Systems

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A control that ensures the asymptotic stability of Takagi–Sugeno fuzzy slow-fast systems with nonlinear subsystems is derived. The set of parameter values for which this feature of these systems remains is estimated.

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References

  1. E. A. Barbashin, Introduction to the Theory of Stability, Wolters-Noordhoff, Groningen (1970).

    MATH  Google Scholar 

  2. A. B. Vasil’eva and V. F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  3. E. I. Gerashchenko and S. M. Gerashchenko, Method of Separation of Motions and Optimization of Nonlinear Systems [in Russian], Nauka, Moscow (1975).

    MATH  Google Scholar 

  4. Lj. T. Grujic, A. A. Martynyuk, and M. Ribbens-Pavella, Large-Scale Systems Stability under Structural and Singular Perturbations, Springer-Verlag, Berlin (1987).

    Book  Google Scholar 

  5. N. N. Krasovskii and A. I. Klimushev, “Uniform asymptotic stability of systems of differential equations with a small parameter in the derivative terms,” J. Appl. Math. Mech., 25, No. 4, 1011–1025 (1961).

    Article  MathSciNet  Google Scholar 

  6. E. F. Mishchenko and N. Kh. Rozov, Differential Equations with a Small Parameter and Relaxation Oscillations [in Russian], Nauka, Moscow (1975).

    MATH  Google Scholar 

  7. L. S. Pontryagin, “Asymptotic behavior of the solutions of systems of differential equations with a small parameter in the higher derivatives,” Amer. Math. Soc. Transl., Ser. 2, 18, 295–319 (1961).

    MathSciNet  MATH  Google Scholar 

  8. A. M. Samoilenko and M. Ya. Svishchuk, “Splitting of a system of differential equations with slowly varying phase in the neighborhood of an asymptotically stable invariant torus,” Ukr. Math. J., 37, No. 6, 617–621 (1985).

    Article  Google Scholar 

  9. A. N. Tikhonov, “Systems of differential equations containing small parameters in the derivatives,” Mat. Sb., 31, No. 3, 576–586 (1952).

    MathSciNet  Google Scholar 

  10. A. S. Khoroshun, “Stability of Takagi–Sugeno fuzzy singularly perturbed systems: Case of stable subsystems,” Dokl. NAN Ukrainy, No. 4, 64–69 (2014).

  11. E. Ya. Antonyuk and A. T. Zabuga, “Motion of an articulated vehicle with two-dimensional sections subject to lateral obstacles,” Int. Appl. Mech., 52, No. 4, 404–412 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  12. W. Assawinchaichote, S. K. Nguang, and P. Shi, “H output feedback control design for uncertain fuzzy singularly perturbed systems an LMI approach,” Automatica, 40, 2147–2152 (2004).

    MathSciNet  MATH  Google Scholar 

  13. W. Assawinchaichote, “An LMI approach of robust H fuzzy state-feedback controller design for HIV/AIDS infection system with dual drag dosages,” World Academy of Science, Eng. Technol. Int. J. Electr. Comput. Eng., 6, No. 5, 1054–1059 (2012).

    Google Scholar 

  14. W. J. Book, “Modeling, design and control of flexible manipulator arms: a tutorial review,” in: Proc. IEEE Decision and Control, December (1990), pp. 500–506.

  15. I. Kanellacopoulos, P. V. Kokotovic, and R. Marino, “An extended direct scheme for robust adaptive nonlinear control,” Automatica, 27, 247–255 (1991).

    Article  MathSciNet  Google Scholar 

  16. A. S. Khoroshun and A. A. Martynyuk, “On stability theory of the uncertain singularly perturbed Takagi-Sugeno systems. The case of unstable subsystems,” Diff. Eqs. Dynam. Syst., 23, No. 4, 423–431 (2015).

    Article  Google Scholar 

  17. L. K. Kuzmina, “General modeling problems in mechanics,” SAMS, 27, 105–118 (1997).

    MATH  Google Scholar 

  18. L. K. Kuzmina, “Asymptotic approach to the general problem of modelling,” Proc. IEEE-SMC, No. 4, 3189–3193 (1998).

  19. V. B. Larin, “Correcting the parameters of undamped mechanical systems,” Int. Appl. Mech., 53, No. 1, 111–115 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  20. V. P. Legeza, “Effectiveness of a roller damper in suppressing conductor galloping,” Int. Appl. Mech., 52, No. 4, 422–431 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  21. S. Mehta and J. Chiasson, “Nonlinear control of a series DC-motor: Theory and experiment,” IEEE Trans. Ind. Electron., 45, 134–141 (1998).

    Article  Google Scholar 

  22. R. Rajesh and M. R. Kaimal, “T–S fuzzy modelwith nonlinear consequence and PDC controller for a class of nonlinear control systems,” Appl. Soft Comput., No. 7, 772–782 (2007).

    Article  Google Scholar 

  23. S. Rao, H. Brandstadter, M. Buss, and V. Utkin, “Sliding mode control in mechanical systems with electric actuators,” in: Proc. Int. Workshop on Variable Structure Systems, Vilanova i la Geltru, Spain, (2004).

  24. A. Sala and C. Arino, “Polynomial fuzzy models for nonlinear control: a Taylor series approach,” IEEE Trans. on Fuzzy Systems, 17, No. 6, 1284–1295 (2009).

    Article  Google Scholar 

  25. A. Siddarth and J. Valasek, “Global tracking control structures for nonlinear perturbed aircraft systems,” in: Proc. CEAS EuroGNC, April (2011), pp. 1–12.

  26. B. Srinivasan, P. Huguenin, and D. Bonvin, “Global stabilization of an inverted pendulum—control strategy and experimental verification,” Automatica, 45, No. 1, 265–269 (2009).

    Article  MathSciNet  Google Scholar 

  27. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and controll,” IEEE Trans. on Systems, Man and Cybernetics, 15, No. 1, 116–132 (1985).

    Article  Google Scholar 

  28. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, New York (2001).

    Book  Google Scholar 

  29. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, “A sum-of-squares approach to moreling and control of nonlinear dynamical systems with polynomial fuzzy systems,” IEEE Trans. on Fuzzy Systems, 17, No. 4, 911–922 (2009).

    Article  Google Scholar 

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Correspondence to A. S. Khoroshun.

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Translated from Prikladnaya Mekhanika, Vol. 54, No. 4, pp. 83–94, July–August, 2018.

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Khoroshun, A.S. Control of Takagi–Sugeno Fuzzy Fast/Slow Systems. Int Appl Mech 54, 443–453 (2018). https://doi.org/10.1007/s10778-018-0897-8

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  • DOI: https://doi.org/10.1007/s10778-018-0897-8

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