Skip to main content
SpringerLink
Log in

Model Predictive Control Based on a Takagi–Sugeno Fuzzy Model for Nonlinear Systems

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper presented a control scheme by imposing a Takagi–Sugeno fuzzy model and the Laguerre functions into the model predictive control for nonlinear systems. The Takagi–Sugeno fuzzy model is an approach by converting a nonlinear system into a linear-like system, which can be easily applied by most of linear control theory. The Laguerre functions can be used to approximate the control signal in the model predictive control, which can reduce the computational cost. To gain the advantages of both approaches, they are integrated into the model predictive control in this paper. Besides, in order to show the control performance of the proposed control scheme, two nonlinear models are selected as illustrative examples, and additional control schemes in the literature are applied to the model so as to compare their performances. The results show that the proposed control scheme provides better performances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Zanon, M., Boccia, A., Palma, V.G.S., Parenti, S., Xausa, I.: Direct optimal control and model predictive control. In: Tonon, D., Aronna, M.S., Kalise, D. (eds.) Optimal Control: Novel Directions and Applications, pp. 263–382. Springer, Berlin (2017)

    Chapter  MATH  Google Scholar 

  2. Cannon, M.: Efficient nonlinear model predictive control algorithms. Annu. Rev. Control 28(2), 229–237 (2004)

    Article  MathSciNet  Google Scholar 

  3. Torrisi, G., Grammatico, S., Smith, R.S., Morari, M.: A variant to sequential quadratic programming for nonlinear model predictive control. In: IEEE 55th Conference on Decision and Control, pp. 2814–2819 (2016)

  4. Tan, Q., Wang, X., Taghia, J., Katupitiya, J.: Force control of two-wheel-steer four-wheel-drive vehicles using model predictive control and sequential quadratic programming for improved path tracking. Int. J. Adv. Robot. Syst. 14(6), 1729881417746295 (2017)

    Article  Google Scholar 

  5. Bryson, A.E., Ho, Y.-C.: Applied optimal control. Hemisphere, London (1975)

    Google Scholar 

  6. Gonzalez, R., Rofman, E.: On deterministic control problems: an approximation procedure for the optimal cost. SIAM J. Control Optim. 23(2), 242–285 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Capuzzo Dolcetta, I.: On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming. Appl. Math. Optim. 10(8), 367–377 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bacic, M., Cannon, M., Kouvaritakis, B.: Extension of efficient predictive control to the nonlinear case. Int. J. Robust Nonlinear Control 15(5), 219–231 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bacic, M., Cannon, M., Kouvaritakis, B.: Constrained NMPC via state-space partitioning for input affine non-linear systems. Int. J. Control 76(15), 1516–1526 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bacic, M., Cannon, M., Lee, Y.I., Kouvaritakis, B.: General interpolation in MPC and its advantages. IEEE Trans. Autom. Control 48(6), 1092–1096 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rossiter, J.A., Ding, Y.: Interpolation methods in model predictive control: an overview. Int. J. Control 83(2), 297–312 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Brockett, R.W.: Feedback invariants for nonlinear systems. IFAC Proc. Vol. 11(1), 1115–1120 (1978)

    Article  Google Scholar 

  13. Slotine, J.-J.E., Li, W.: Applied nonlinear control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  14. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  15. Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst. 45(2), 135–156 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, H.O., Tanaka, K., Griffin, M.: Parallel distributed compensation of nonlinear systems by Takagi–Sugeno fuzzy model. In: IEEE International Joint Conference of the Fourth International Conference on Fuzzy Systems and the Second International Fuzzy Engineering Symposium, vol. 2, pp. 531–538 (1995)

  17. Nguyen, A.T., Márquez, R., Guerra, T.M., Dequidt, A.: Improved LMI conditions for local quadratic stabilization of constrained Takagi–Sugeno fuzzy systems. Int. J. Fuzzy Syst. 19(1), 225–237 (2017)

    Article  MathSciNet  Google Scholar 

  18. Kchaou, M.: Robust H∞ 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 

  19. Bourahala, F., Guelton, K., Manamanni, N., Khaber, F.: Relaxed controller design conditions for Takagi–Sugeno systems with state time-varying delays. Int. J. Fuzzy Syst. 19(5), 1406–1416 (2017)

    Article  MathSciNet  Google Scholar 

  20. Elleuch, I., Khedher, A., Othman, K.B.: State and faults estimation based on proportional integral sliding mode observer for uncertain Takagi-Sugeno fuzzy systems and its application to a turbo-reactor. Int. J. Fuzzy Syst. 19(6), 1768–1781 (2017)

    Article  MathSciNet  Google Scholar 

  21. Schrodt, A., Kroll, A.: On iterative closed-loop identification using affine Takagi–Sugeno models and controllers. Int. J. Fuzzy Syst. 19(6), 1978–1988 (2017)

    Article  MathSciNet  Google Scholar 

  22. Benzaouia, A., El Hajjaji, A.: Conditions of stabilization of positive continuous Takagi–Sugeno fuzzy systems with delay. Int. J. Fuzzy Syst. 20(3), 750–758 (2018)

    Article  MathSciNet  Google Scholar 

  23. Li, J., Niemann, D., Wang, H.O., Tanaka, K.: Parallel distributed compensation for Takagi–Sugeno fuzzy models: multiobjective controller design. In: American Control Conference, vol. 3, pp. 1832–1836 (1999)

  24. Akar, M., Ozguner, U.: Decentralized parallel distributed compensator design for Takagi–Sugeno fuzzy systems. In: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 5, pp. 4834–4839 (1999)

  25. Li, J., Wang, H.O., Niemann, D., Tanaka, K.: Dynamic parallel distributed compensation for Takagi–Sugeno fuzzy systems: an LMI approach. Inf. Sci. 123(3), 201–221 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Amiri-M, A.A., Moavenian, M., Torabiz, K.: Takagi–Sugeno fuzzy modelling and parallel distributed compensation control of conducting polymer actuators. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 224(1), 41–51 (2010)

    Article  Google Scholar 

  27. Sadeghi, M.S., Safarinejadian, B., Farughian, A.: Parallel distributed compensator design of tank level control based on fuzzy Takagi–Sugeno model. Appl. Soft Comput. 21, 280–285 (2014)

    Article  Google Scholar 

  28. Nguyen, A.T., Dambrine, M., Lauber, J.: Simultaneous design of parallel distributed output feedback and anti-windup compensators for constrained Takagi–Sugeno fuzzy systems. Asian J. Control. 18(5), 1641–1654 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sarimveis, H., Bafas, G.: Fuzzy model predictive control of non-linear processes using genetic algorithms. Fuzzy Sets Syst. 139(1), 59–80 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  30. Roubos, J.A., Mollov, S., Babuška, R., Verbruggen, H.B.: Fuzzy model-based predictive control using Takagi–Sugeno models. Int. J. Approx. Reason. 22(1–2), 3–30 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. Li, N., Li, S.Y., Xi, Y.G.: Multi-model predictive control based on the Takagi–Sugeno fuzzy models: a case study. Inf. Sci. 165(3), 247–263 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ding, B.: Dynamic output feedback predictive control for nonlinear systems represented by a Takagi–Sugeno model. IEEE Trans. Fuzzy Syst. 19(5), 831–843 (2011)

    Article  Google Scholar 

  33. Ding, B., Ping, X.: Output feedback predictive control with one free control move for nonlinear systems represented by a Takagi–Sugeno model. IEEE Trans. Fuzzy Syst. 21(5), 1–15 (2013)

    Article  Google Scholar 

  34. Yang, W., Feng, G., Zhang, T.: Robust model predictive control for discrete-time Takagi–Sugeno fuzzy systems with structured uncertainties and persistent disturbances. IEEE Trans. Fuzzy Syst. 22(5), 1213–1228 (2014)

    Article  Google Scholar 

  35. Wang, M., Paulson, J.A., Yan, H., Shi, H.: An adaptive model predictive control strategy for nonlinear distributed parameter systems using the type-2 Takagi–Sugeno model. Int. J. Fuzzy Syst. 18(5), 792–805 (2016)

    Article  MathSciNet  Google Scholar 

  36. Ariño, C., Querol, A., Sala, A.: Shape-independent model predictive control for Takagi–Sugeno fuzzy systems. Eng. Appl. Artif. Intell. 65, 493–505 (2017)

    Article  Google Scholar 

  37. Boulkaibet, I., Belarbi, K., Bououden, S., Marwala, T., Chadli, M.: A new TS fuzzy model predictive control for nonlinear processes. Expert Syst. Appl. 88, 132–151 (2017)

    Article  Google Scholar 

  38. Shi, K., Wang, B., Yang, L., Jian, S., Bi, J.: Takagi–Sugeno fuzzy generalized predictive control for a class of nonlinear systems. Nonlinear Dyn. 89, 169–177 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yang, J., Li, X., Mou, H.G., Jian, L.: Predictive control of solid oxide fuel cell based on an improved Takagi–Sugeno fuzzy model. J. Power Sources 193(2), 699–705 (2009)

    Article  Google Scholar 

  40. Benitez-Pérez, H., Ortega-Arjona, J., Cardenas-Flores, F., Quiñones-Reyes, P.: Reconfiguration control strategy using Takagi–Sugeno model predictive control for network control systems-a magnetic levitation case study. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 224, 1022–1032 (2010)

    Article  Google Scholar 

  41. Feng, X., Patton, R., Wang,: Z. Sensor fault tolerant control of a wind turbine via Takagi–Sugeno fuzzy observer and model predictive control. In: UKACC International Conference on Control, pp. 480–485 (2014)

  42. Khooban, M.H., Vafamand, N., Niknam, T., Dragicevic, T., Blaabjerg, F.: Model-predictive control based on Takagi–Sugeno fuzzy model for electrical vehicles delayed model. ET Electr. Power Appl. 11(5), 918–934 (2017)

    Article  Google Scholar 

  43. Franco, I.C., Schmitz, J.E., Costa, T.V., Fileti, A.M.F., Silva, F.V.: Development of a predictive control based on Takagi–Sugeno model applied in a nonlinear system of industrial refrigeration. Chem. Eng. Commun. 204(1), 39–54 (2017)

    Article  Google Scholar 

  44. Broome, P.W.: Discrete orthonormal sequences. J. ACM 12(2), 151–168 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  45. Weeks, W.T.: Numerical inversion of Laplace transforms using Laguerre functions. J. ACM 13(3), 419–429 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  46. Heuberger, P.S., Van den Hof, P.M., Bosgra, O.H.: A generalized orthonormal basis for linear dynamical systems. IEEE Trans. Autom. Control 40(3), 451–465 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang, H., Chen, Z., Wang, Y., Li, M., Qin, T.: Adaptive predictive control algorithm based on Laguerre functional model. Int. J. Adapt. Control Signal Process. 20(2), 53–76 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  48. Abdullah, M., Idres, M.: Fuel cell starvation control using model predictive technique with Laguerre and exponential weight functions. J. Mech. Sci. Technol. 28(5), 1995–2002 (2014)

    Article  Google Scholar 

  49. Chipofya, M., Lee, D.J., Chong, K.T.: Trajectory tracking and stabilization of a quadrotor using model predictive control of Laguerre functions. Abstr. Appl. Anal. 2015, 916864 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  50. Benlahrache, M.A., Othman, S., Sheibat-Othman, N.: Multivariable model predictive control of wind turbines based on Laguerre functions. Wind Eng. 41(6), 409–420 (2017)

    Article  Google Scholar 

  51. Zheng, Y., Zhou, J., Xu, Y., Zhang, Y., Qian, Z.: A distributed model predictive control based load frequency control scheme for multi-area interconnected power system using discrete-time Laguerre functions. ISA Trans. 68, 127–140 (2017)

    Article  Google Scholar 

  52. Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2004)

    Google Scholar 

  53. Wang, L.: Discrete model predictive controller design using Laguerre functions. J. Process Control 14(2), 131–142 (2004)

    Article  Google Scholar 

  54. Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer Science & Business Media, Berlin (2009)

    MATH  Google Scholar 

  55. Wang, H.O., Tanaka, K., Griffin, M.: An analytical framework of fuzzy modeling and control of nonlinear systems: stability and design issues. In: Proceedings of the American Control Conference, vol. 3, pp. 2272–2276 (1995)

  56. Wang, D., Huang, J.: A neural network-based approximation method for discrete-time nonlinear servomechanism problem. IEEE Trans. Neural Netw. 12(3), 591–597 (2001)

    Article  Google Scholar 

  57. Xia, Y., Yang, H., Shi, P., Fu, M.: Constrained infinite-horizon model predictive control for fuzzy-discrete-time systems. IEEE Trans. Fuzzy Syst. 18(2), 429–436 (2010)

    Google Scholar 

  58. Slotine, J.-J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  59. Zhang, B.: Stability control of flexible joint robot based TS fuzzy model using fuzzy Lyapunov function. J. Converg. Inf. Technol. 8(1), 60–68 (2013)

    Google Scholar 

Download references

Acknowledgements

The study was sponsored by a Grant, MOST 104-2221-E-011-040, from the Ministry of Science and Technology, Taiwan.

Author information

Authors and Affiliations

  1. Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, Taipei, 10607, Taiwan

    Yong-Lin Kuo & Ilmiyah Elrosa Citra Resmi

Authors
  1. Yong-Lin Kuo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ilmiyah Elrosa Citra Resmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong-Lin Kuo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuo, YL., Citra Resmi, I.E. Model Predictive Control Based on a Takagi–Sugeno Fuzzy Model for Nonlinear Systems. Int. J. Fuzzy Syst. 21, 556–570 (2019). https://doi.org/10.1007/s40815-018-0574-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-018-0574-4

Keywords

Search

Navigation