Fuzzy modeling and synchronization of hyperchaotic systems. (English) Zbl 1093.93540

Summary: This paper presents fuzzy model-based designs for synchronization of hyperchaotic systems. The T-S fuzzy models for hyperchaotic systems are exactly derived. Based on the T-S fuzzy hyperchaotic models, the fuzzy controllers for hyperchaotic synchronization are designed via the exact linearization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed method.


93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic systems, Phys rev lett, 64, 821-824, (1990) · Zbl 0938.37019
[2] Carroll, T.L.; Pecora, L.M., Synchronizing chaotic circuits, IEEE trans CAS I, 38, 453-456, (1991)
[3] Ogorzalek, J., Taming chaos. part I. synchronization, IEEE trans CAS I, 40, 693-699, (1993) · Zbl 0850.93353
[4] Pecora, L.M.; Carroll, T.L.; Johnson, G.A.; Mar, D.J.; Heagy, J.F., Fundamentals of synchronization in chaotic systems, concepts, and applications, Chaos, 7, 520-543, (1997) · Zbl 0933.37030
[5] Chen, G.; Dong, X., From chaos to order methodologies, perspectives and applications, Nonlinear science, (1998), World Scientific Singapore
[6] Lakshmanan, M.; Murali, K., Chaos in nonlinear oscillators: controlling and synchronization, (1996), World Scientific Singapore · Zbl 0868.58058
[7] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D.L.; Zhou, C.S., The synchronization of chaotic systems, Phys rep, 366, 1-101, (2002) · Zbl 0995.37022
[8] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE trans CAS, 44, 1143-1147, (1997)
[9] Grassi, G.; Mascolo, S., Synchronizing hyperchaotic systems by observer design, IEEE trans CAS, 46, 1135-1138, (1999) · Zbl 1159.94361
[10] Tanaka, K.; Ikeda, T.; Wang, H.O., A unified approach to controlling chaos via an LMI-based fuzzy control system design, IEEE trans CAS, 45, 1021-1040, (1998) · Zbl 0951.93046
[11] Lian, K.Y.; Chiu, C.S.; Chiang, T.S.; Liu, P., LMI-based fuzzy chaotic synchronization and communications, IEEE trans fuzzy syst, 9, 539-553, (2001)
[12] Wang, Y.W.; Guan, Z.H.; Wang, H.O., LMI-based fuzzy stability and synchronization of chen’s system, Phys lett A, 320, 154-159, (2003) · Zbl 1065.37503
[13] Xue, Y.J.; Yang, S.Y., Synchronization of generalized henon map by using adaptive fuzzy controller, Chaos, solitons & fractals, 17, 717-722, (2003) · Zbl 1043.93519
[14] Tanaka, K.; Wang, H.O., Fuzzy control system design and analysis: a linear matrix inequality approach, (2001), Wiley New York
[15] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE tans syst man cyb, 15, 116-132, (1985) · Zbl 0576.93021
[16] Rössler, O.E., An equation for hyperchaos, Phys lett A, 71, 155-159, (1979) · Zbl 0996.37502
[17] Matsumoto, T.; Chua, L.O.; Kobayashi, K., Hyperchaos: laboratory experiment and numerical confirmation, IEEE trans CAS, 33, 1143-1147, (1986)
[18] Tamasevicius A. Hyperchaotic circuits: state of the art. Proceedings of NDES’97, Moscow, Russia, 1997. p. 97-102
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