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Universal fuzzy controllers based on generalized T-S fuzzy models. (English) Zbl 1251.93069
Summary: This paper investigates the universal fuzzy control problem based on generalized T-S fuzzy models. The universal approximation capability of the generalized T-S fuzzy models is shown and an approach to robust controller design for general nonlinear systems based on this kind of generalized T-S fuzzy models is developed. The results of universal fuzzy controllers for two classes of nonlinear systems are then given, and constructive procedures to obtain the universal fuzzy controllers are also provided. An example is finally presented to show the effectiveness of our approach.

MSC:
93C42 Fuzzy control/observation systems
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[1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. syst. man cybernet.: part B: cybernet., 15, 1, 116-132, (1985) · Zbl 0576.93021
[2] Tanaka, K.; Wang, H.O., Fuzzy control systems design and analysis: A LMI approach, (2001), Wiley New York
[3] Tong, S.; Li, C., Fuzzy adaptive observer backstepping control for MIMO nonlinear systems, Fuzzy sets syst., 160, 19, 2755-2775, (2009) · Zbl 1176.93049
[4] Liu, J.; Wang, W.; Golnaraghi, F.; Kubica, E., A novel fuzzy framework for nonlinear system control, Fuzzy sets syst., 161, 21, 2746-2759, (2010) · Zbl 1206.93065
[5] Qiu, J.; Feng, G.; Yang, J., A new design of delay-dependent robust H-infinity filtering for discrete-time T-S fuzzy systems with time-varying delay, IEEE trans. fuzzy syst., 17, 5, 1044-1058, (2009)
[6] Qiu, J.; Feng, G.; Gao, H., Fuzzy-model-based piecewise H-infinity static output feedback controller design for networked nonlinear systems, IEEE trans. fuzzy syst., 18, 5, 919-934, (2010)
[7] Liu, Y.; Tong, S.; Li, T., Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems, Fuzzy sets syst., 164, 1, 25-44, (2011) · Zbl 1217.93090
[8] Leu, Y., Mean-based fuzzy identifier and control of uncertain nonlinear systems, Fuzzy sets syst., 161, 6, 837-858, (2010) · Zbl 1217.93088
[9] Dong, J.; Yang, G., Dynamic output feedback H∞ control synthesis for discrete-time T-S fuzzy systems via switching fuzzy controllers, Fuzzy sets syst., 160, 4, 482-499, (2009) · Zbl 1175.93122
[10] Feng, G., A survey on analysis and design of model-based fuzzy control systems, IEEE trans. fuzzy syst., 14, 5, 676-697, (2006)
[11] Johansson, M.; Rantzer, A.; Årzén, K.-E., Piecewise quadratic stability of fuzzy systems, IEEE trans.fuzzy syst., 7, 6, 713-722, (1999)
[12] Tanaka, K.; Ohtake, H.; Wang, H.O., A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions, IEEE trans. fuzzy syst., 15, 3, 333-341, (2007)
[13] Chen, C.L.; Feng, G.; Sun, D.; Guan, X.P., Output feedback control for discrete time fuzzy systems with application to chaos control, IEEE trans. fuzzy syst., 13, 4, 531-543, (2005)
[14] Feng, G., Analysis and synthesis of fuzzy control systems: A model-based approach, (2010), CRC Press Boca Raton, FL
[15] Buckley, J.J., Universal fuzzy controllers, Automatica, 28, 6, 1245-1248, (1992) · Zbl 0775.93133
[16] Buckley, J.J., Sugeno type controllers are universal controllers, Fuzzy sets syst., 53, 10, 299-303, (1993) · Zbl 0785.93057
[17] Buckley, J.J.; Hayashi, Y., Fuzzy input – output controllers are universal approximators, Fuzzy sets syst., 58, 3, 273-278, (1993) · Zbl 0793.93078
[18] Ying, H., General takagi – sugeno fuzzy systems with simplified linear rule consequent are universal controllers, models and filters, Inf. sci., 108, 1-4, 91-107, (1998) · Zbl 0928.93034
[19] Cao, S.G.; Rees, N.W.; Feng, G., Universal fuzzy controllers for a class of nonlinear systems, Fuzzy sets syst., 122, 1, 117-123, (2001) · Zbl 0980.93038
[20] Cao, S.G.; Rees, N.W.; Feng, G., Mamdani-type fuzzy controllers are universal fuzzy controllers, Fuzzy sets syst., 123, 3, 359-367, (2001) · Zbl 0999.93040
[21] Zeng, X.-J.; Singh, M.G., Approximation theory of fuzzy systems—SISO case, IEEE trans. fuzzy syst., 2, 2, 162-176, (1994)
[22] Zeng, X.-J.; Singh, M.G., Approximation theory of fuzzy systems—MIMO case, IEEE trans. fuzzy syst., 3, 2, 219-235, (1995)
[23] X.-J. Zeng, J.A. Keane, D. Wang, Fuzzy systems approach to approximation and stabilization of conventional affine nonlinear systems, in: Proceedings of the 2006 IEEE International Conference on Fuzzy Systems, Vancouver, BC, Canada, 2006, pp. 277-284.
[24] Hahn, W., Stability of motion, (1968), Berlin Springer · Zbl 0172.12504
[25] Q. Gao, X.-J. Zeng, G. Feng, Y. Wang, T-S fuzzy systems approach to approximation and robust controller design for general nonlinear systems, in: Proceedings of the 2011 IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, 2011, pp. 1299-1304.
[26] Sontag, E.D.; Wang, Y., On characterizations of the input-to-state stability property, Syst. control lett., 24, 5, 351-359, (1995) · Zbl 0877.93121
[27] Lin, Y.D.; Sontag, E.D.; Wang, Y., A smooth converse Lyapunov theorem for robust stability, SIAM J. control optim., 34, 1, 124-160, (1996) · Zbl 0856.93070
[28] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[29] A. Young, C.Y. Cao, N. Hovakimyan, E. Lavretsky, Control of a nonaffine double-pendulum system via dynamic inversion and time-scale separation, in: Proceedings of the 2006 American Control Conference, Minneapolis, MN, USA, 2006, pp. 1820-1825.
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