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.
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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)
Cannon, M.: Efficient nonlinear model predictive control algorithms. Annu. Rev. Control 28(2), 229–237 (2004)
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)
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)
Bryson, A.E., Ho, Y.-C.: Applied optimal control. Hemisphere, London (1975)
Gonzalez, R., Rofman, E.: On deterministic control problems: an approximation procedure for the optimal cost. SIAM J. Control Optim. 23(2), 242–285 (1985)
Capuzzo Dolcetta, I.: On a discrete approximation of the Hamilton–Jacobi equation of dynamic programming. Appl. Math. Optim. 10(8), 367–377 (1983)
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)
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)
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)
Rossiter, J.A., Ding, Y.: Interpolation methods in model predictive control: an overview. Int. J. Control 83(2), 297–312 (2010)
Brockett, R.W.: Feedback invariants for nonlinear systems. IFAC Proc. Vol. 11(1), 1115–1120 (1978)
Slotine, J.-J.E., Li, W.: Applied nonlinear control. Prentice Hall, Englewood Cliffs (1991)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)
Tanaka, K., Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst. 45(2), 135–156 (1992)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Sarimveis, H., Bafas, G.: Fuzzy model predictive control of non-linear processes using genetic algorithms. Fuzzy Sets Syst. 139(1), 59–80 (2003)
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)
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)
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)
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)
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)
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)
Ariño, C., Querol, A., Sala, A.: Shape-independent model predictive control for Takagi–Sugeno fuzzy systems. Eng. Appl. Artif. Intell. 65, 493–505 (2017)
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)
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)
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)
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)
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)
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)
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)
Broome, P.W.: Discrete orthonormal sequences. J. ACM 12(2), 151–168 (1965)
Weeks, W.T.: Numerical inversion of Laplace transforms using Laguerre functions. J. ACM 13(3), 419–429 (1966)
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)
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)
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)
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)
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)
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)
Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2004)
Wang, L.: Discrete model predictive controller design using Laguerre functions. J. Process Control 14(2), 131–142 (2004)
Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer Science & Business Media, Berlin (2009)
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)
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)
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)
Slotine, J.-J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)
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)
Acknowledgements
The study was sponsored by a Grant, MOST 104-2221-E-011-040, from the Ministry of Science and Technology, Taiwan.
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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
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DOI: https://doi.org/10.1007/s40815-018-0574-4