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International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 556–570 | Cite as

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

  • Yong-Lin KuoEmail author
  • Ilmiyah Elrosa Citra Resmi
Article
  • 48 Downloads

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.

Keywords

Model predictive control T–S fuzzy model Laguerre function 

Notes

Acknowledgements

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

References

  1. 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)Google Scholar
  2. 2.
    Cannon, M.: Efficient nonlinear model predictive control algorithms. Annu. Rev. Control 28(2), 229–237 (2004)MathSciNetGoogle Scholar
  3. 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)Google Scholar
  4. 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)Google Scholar
  5. 5.
    Bryson, A.E., Ho, Y.-C.: Applied optimal control. Hemisphere, London (1975)Google Scholar
  6. 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)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Capuzzo Dolcetta, I.: On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming. Appl. Math. Optim. 10(8), 367–377 (1983)MathSciNetzbMATHGoogle Scholar
  8. 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)MathSciNetzbMATHGoogle Scholar
  9. 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)MathSciNetzbMATHGoogle Scholar
  10. 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)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Rossiter, J.A., Ding, Y.: Interpolation methods in model predictive control: an overview. Int. J. Control 83(2), 297–312 (2010)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Brockett, R.W.: Feedback invariants for nonlinear systems. IFAC Proc. Vol. 11(1), 1115–1120 (1978)Google Scholar
  13. 13.
    Slotine, J.-J.E., Li, W.: Applied nonlinear control. Prentice Hall, Englewood Cliffs (1991)zbMATHGoogle Scholar
  14. 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)zbMATHGoogle Scholar
  15. 15.
    Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst. 45(2), 135–156 (1992)MathSciNetzbMATHGoogle Scholar
  16. 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)Google Scholar
  17. 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)MathSciNetGoogle Scholar
  18. 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)MathSciNetGoogle Scholar
  19. 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)MathSciNetGoogle Scholar
  20. 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)MathSciNetGoogle Scholar
  21. 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)MathSciNetGoogle Scholar
  22. 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)MathSciNetGoogle Scholar
  23. 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)Google Scholar
  24. 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)Google Scholar
  25. 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)MathSciNetzbMATHGoogle Scholar
  26. 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)Google Scholar
  27. 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)Google Scholar
  28. 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)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Sarimveis, H., Bafas, G.: Fuzzy model predictive control of non-linear processes using genetic algorithms. Fuzzy Sets Syst. 139(1), 59–80 (2003)MathSciNetzbMATHGoogle Scholar
  30. 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)MathSciNetzbMATHGoogle Scholar
  31. 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)MathSciNetzbMATHGoogle Scholar
  32. 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)Google Scholar
  33. 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)Google Scholar
  34. 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)Google Scholar
  35. 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)MathSciNetGoogle Scholar
  36. 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)Google Scholar
  37. 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)Google Scholar
  38. 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)MathSciNetzbMATHGoogle Scholar
  39. 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)Google Scholar
  40. 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)Google Scholar
  41. 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)Google Scholar
  42. 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)Google Scholar
  43. 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)Google Scholar
  44. 44.
    Broome, P.W.: Discrete orthonormal sequences. J. ACM 12(2), 151–168 (1965)MathSciNetzbMATHGoogle Scholar
  45. 45.
    Weeks, W.T.: Numerical inversion of Laplace transforms using Laguerre functions. J. ACM 13(3), 419–429 (1966)MathSciNetzbMATHGoogle Scholar
  46. 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)MathSciNetzbMATHGoogle Scholar
  47. 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)MathSciNetzbMATHGoogle Scholar
  48. 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)Google Scholar
  49. 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)MathSciNetzbMATHGoogle Scholar
  50. 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)Google Scholar
  51. 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)Google Scholar
  52. 52.
    Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2004)Google Scholar
  53. 53.
    Wang, L.: Discrete model predictive controller design using Laguerre functions. J. Process Control 14(2), 131–142 (2004)Google Scholar
  54. 54.
    Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer Science & Business Media, Berlin (2009)zbMATHGoogle Scholar
  55. 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)Google Scholar
  56. 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)Google Scholar
  57. 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. 58.
    Slotine, J.-J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)zbMATHGoogle Scholar
  59. 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

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate Institute of Automation and ControlNational Taiwan University of Science and TechnologyTaipeiTaiwan

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