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Profoundly Robust Controlling Strategy for Uncertain Nonlinear Mimo System Using T–S Fuzzy System

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Abstract

In this paper, we addressed the problem of developing a robust control scheme for the MIMO nonlinear system; to achieve this, we adopt nonlinear systems with plant uncertainties, time-delayed uncertainties, and external disturbances. A fuzzy logic system is used to approximate the unknown nonlinear functions, and a Takagi–Sugeno (T–S) fuzzy observer is presented for state estimations. The designed control law works on basis of indirect T–S fuzzy control and utilizes two online approximations which allowed instantaneous insertion of finding gains of delayed state uncertainties. The benefit of employing a T–S fuzzy system is utilize of analytical results which are linear instead of approximating functions of nonlinear system with online update laws. The T–S fuzzy tracking control utilizes variable structure control method to resolve the system uncertainties, time-delayed uncertainty, and the external disturbances such that H ∞ tracking performance is achieved. The control rules are derived based on a Lyapunov criterion and the Riccati inequality such that all states of the system are uniformly ultimately limited. Therefore, the effect can be reduced to any prescribed level to achieve H ∞ tracking performance. A two-connected inverted pendulums system on carts used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.

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References

  1. Ho, W.H., Chen, S.H., Chou, J.H.: Observability robustness of uncertain fuzzy-model-based control systems. Int. J. Innov. Comput. Inf. Control 9(2), 805–819 (2013)

    Google Scholar 

  2. Lin, H., Xu, Y., Zhao, Y.: Frequency analysis of TS fuzzy control systems. Int. J. Innov. Comput. Inf. Control 9(12), 4781–4791 (2013)

    Google Scholar 

  3. Boulkroune, A., Tadjine, M., M’Saad, M., Farza, M.: Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction. Fuzzy Sets Syst. 161(6), 797–820 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boulkroune, A., M’saad, M.: On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign. Fuzzy Sets Syst. 201, 71–85 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Nekoukar, V., Erfanian, A.: Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems. Fuzzy Sets Syst. 179(1), 34–49 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 40(1), 170–184 (2010)

    Article  Google Scholar 

  7. Tong, S., Sui, S., Li, Y.: Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans. Fuzzy Syst. 23(4), 729–742 (2015)

    Article  Google Scholar 

  8. Chang, Y.C.: An adaptive H ∞ tracking control for a class of nonlinear multiple-input multiple-output (MIMO) systems. IEEE Trans. Autom. Control 46(9), 1432–1437 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Essounbouli, N., Hamzaoui, A., Zaytoon, J.: An improved robust adaptive fuzzy controller for MIMO systems. Control Intell. Syst. 34(1), 12–21 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Ge, S.S., Zhang, J.: Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback. IEEE Trans. Neural Netw. 14(4), 900–918 (2003)

    Article  Google Scholar 

  11. Kung, C.C., Chen, T.H.: Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems. Fuzzy Sets Syst. 155(2), 292–308 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Koshkouei, A.J., Zinober, A.S.I.: Partial Lipschitz nonlinear sliding mode observers. In: Proceedings of the 7th Mediterranean Conference on Control and Automation (MED’99), 2350–2359 (1999)

  13. Fang, C.H., Liu, Y.S., Kau, S.W., Hong, L., Lee, C.H.: A new LMI-based approach to relaxed quadratic stabilization of TS fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(3), 386–397 (2006)

    Article  Google Scholar 

  14. Asemani, M.H., Majd, V.J.: A robust H ∞ observer-based controller design for uncertain T–S fuzzy systems with unknown premise variables via LMI. Fuzzy Sets Syst. 212, 21–40 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gao, Z., Shi, X., Ding, S.X.: Fuzzy state/disturbance observer design for T–S fuzzy systems with application to sensor fault estimation. IEEE Trans. Syst. Man Cybern. B Cybern. 38(3), 875–880 (2008)

    Article  Google Scholar 

  16. Rhee, B.J., Won, S.: A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design. Fuzzy Sets Syst. 157(9), 1211–1228 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gao, Z., Ding, S.X.: Fault reconstruction for Lipschitz nonlinear descriptor systems via linear matrix inequality approach. Circuits Syst. Signal Process. 27(3), 295–308 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fridman, E., Shaked, U.: A descriptor system approach to H ∞ control of linear time-delay systems. IEEE Trans. Autom. Control 47(2), 253–270 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ilhem, K., Dalel, J., Saloua, B.H.A., Naceur, A.M.: Observer design for Takagi–Sugeno descriptor system with Lipschitz constraints. Int. J. Instrum. Control Syst. 2(2), 13–25 (2012)

    Google Scholar 

  20. Tong, S., Yang, G., Zhang, W.: Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays. Int. J. Appl. Math. Comput. Sci. 21(4), 617–627 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, H., Pan, Y., Yu, Z., Zhao, X., Yang, X.: Fuzzy output-feedback control for non-linear systems with input time-varying delay. IET Control Theory Appl. 8(9), 738–745 (2014)

    Article  MathSciNet  Google Scholar 

  22. Kumaresan, N., Ratnavelu, K.: Optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno fuzzy system with singular cost using genetic programming. Appl. Soft Comput. 24, 1136–1144 (2014)

    Article  Google Scholar 

  23. Li, Y., Tong, S., Li, T.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2015)

    Article  Google Scholar 

  24. Li, Y., Tong, S., Li, T.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybern. 45(1), 138–149 (2015)

    Article  Google Scholar 

  25. Klug, M., Castelan, E.B., Leite, V.J.S., Silva, L.F.P.: Fuzzy dynamic output feedback control through nonlinear Takagi–Sugeno models. Fuzzy Sets Syst. 263, 92–111 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Chang, Y.C.: Robust tracking control for nonlinear MIMO systems via fuzzy approaches. Automatica 36(10), 1535–1545 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  27. Park, J.H., Park, G.T., Kim, S.H., Moon, C.J.: Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer. Fuzzy Sets Syst. 151(1), 21–42 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu, Y.J., Tong, S.C., Li, T.S.: Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst. 164(1), 25–44 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. Xie, X., Yue, D., Ma, T., Zhu, X.: Further studies on control synthesis of discrete-time TS fuzzy systems via augmented multi-indexed matrix approach. IEEE Trans. Cybern. 44(12), 2784–2791 (2014)

    Article  Google Scholar 

  30. Xie, X., Yue, D., Zhang, H., Xue, Y.: Control synthesis of discrete-time T–S fuzzy systems via a multi-instant homogenous polynomial approach. IEEE Trans. Cybern. 46(3), 630–640 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Anjuman Institute of Technology and Management, Bhatkal, Karnataka, India

    A. K. Iqbal Ahammed

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  1. A. K. Iqbal Ahammed
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Correspondence to A. K. Iqbal Ahammed.

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Iqbal Ahammed, A.K. Profoundly Robust Controlling Strategy for Uncertain Nonlinear Mimo System Using T–S Fuzzy System. Int. J. Fuzzy Syst. 19, 1104–1117 (2017). https://doi.org/10.1007/s40815-016-0225-6

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  • DOI: https://doi.org/10.1007/s40815-016-0225-6

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