Chaotifying fuzzy hyperbolic model using impulsive and nonlinear feedback control approaches

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 8, 2005, Pages 2603-2610

  Zhang, Huaguang ^a   Wang, Zhiliang ^a   Liu, Derong ^b  

^a NORTHEASTERN UNIVERSITY   (China)

^b University of Illinois at Chicago   (United States)

Author keywords

Chaotification; Devaney's chaos; Fuzzy hyperbolic model; Impulsive control; Poincar section

Indexed keywords

EID: 25844502616     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740501354X     Document Type: Article

References (38)

1. Chen, G. & Lai, D. [1997] "Making a dynamical system chaotic: Feedback control of Lyapunov exponents for discrete-time dynamical systems," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 44, 250-253.
2. Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives, and Applications (World Scientific, Singapore).
3. Chen, G. & Lai, D. [1998] "Feedback anticontrol of discrete chaos," Int. J. Bifurcation and Chaos 8, 1585-1590.
4. Chen, G., Fan, J.-Q., Hong, Y. & Qin, H. S. [2001] "Introduction to chaos control and anti-control," in Advanced Topics in Nonlinear Control Systems, eds. Leung, T. P. & Qin, H.-S. (World Scientific, Singapore), Chap. 6, pp. 193-245.
5. Chen, L. & Chen, G. [1999] "Fuzzy predictive control of uncertain chaotic systems using time series," Int. J. Bifurcation and Chaos 9, 757-767.
6. Devaney, R. L. [1987] An Introduction to Chaotic Dynamical Systems (Addison-Wesley, NY).
7. Guan, Z. H., Chen, G. & Ueta, T. [2000] "On impulsive control of a periodically forced chaotic pendulum system," IEEE Trans. Autom. Contr. 45, 1724-1727.
8. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
9. Hirsch, M. W. & Smale, S. [1974] Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, NY).
10. Kaszkurewicz, E. & Bhaya, A. [2000] Matrix Diagonal Stability in Systems and Computation (Birkhäuser, Boston).
11. Khalil, H. K. [2002] Nonlinear Systems, 3rd edition (Prentice Hall, NJ).
12. Li, Z., Halang, W., Chen, G. & Tian, L. F. [2003] "Chaotifying continuous-time Takagi-Sugeno fuzzy systems via time-delayed feedback," Dyn. Contin. Discr. Impul. Syst. 10, 813-832.
13. Li, Z. G., Wen, C. Y., Soh, Y. C. & Xie, W. X. [2001] "The stabilization and synchronization of Chua's oscillators via impulsive control," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 48, 1351-1355.
14. Lü, J. H., Zhou, T. S., Chen, G. & Yang, X. S. [2002] "Generating chaos with a switching piecewise-linear controller," Chaos 12, 344-349.
15. Passino, K. M. & Yurkovich, S. [1998] Fuzzy Control (Addison Wesley, Reading, MA).
16. Sanchez, E. N., Perez, J. P. & Chen, G. [2001] "Using dynamic neural networks to generate chaos: An inverse optimal control approach," Int. J. Bifurcation and Chaos 11, 857-863.
17. Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. [1994] "Controlling chaos in the brain," Nature 370, 615-620.
18. ∞ synchronization of chaotic Lur'e systems," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 44, 891-904.
19. ∞ synchronization of chaotic Lur'e systems," Int. J. Bifurcation and Chaos 7, 1323-1335.
20. Suykens, J. A. K., Yang, T. & Chua, L. O. [1998] "Impulsive synchronization of chaotic Lur'e systems by measurement feedback," Int. J. Bifurcation and Chaos 8, 1371-1381.
21. Suykens, J. A. K., Curran, P. F. & Chua, L. O. [1999] "Robust synthesis for master-slave synchronization of Lur'e systems," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 46, 841-850.
22. Tanaka, K., Ikeda, T. & Wang, H. O. [1998] "A unified approach to controlling chaos via an LMI-based fuzzy control system design," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 45, 1021-1040.
23. Tang, K. S., Man, K. F., Zhong, G. Q. & Chen, G. [2001] "Generating chaos via x|x|," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 48, 636-641.
24. Wang, X. F. & Chen, G. [1999] "On feedback anticontrol of discrete chaos," Int. J. Bifurcation and Chaos 9, 1435-1441.
25. Wang, X. F. & Chen, G. [2000a] "Chaotifying a stable LTI system by tiny feedback control," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 47, 410-415.
26. Wang, X. F. & Chen, G. [2000b] "Chaotifying a stable map via smooth small-amplitude high-frequency feedback control," Int. J. Circuit Th. Appl. 28, 305-312.
27. Wang, X. F. & Chen, G. [2000c] "Chaotification via arbitrarily small feedback controls: Theory, method, and applications," Int. J. Bifurcation and Chaos 10, 549-570.
28. Wang, X. F., Chen, G. & Yu, X. [2000] "Anticontrol of chaos in continuous-time systems via time-delay feedback," Chaos 10, 771-779.
29. Wang, X. F., Chen, G. & Man, K. F. [2001] "Making a continuous-time minimum-phase system chaotic by using time-delay feedback," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 48, 641-645.
30. Yang, L., Liu, Z. & Chen, G. [2002] "Chaotifying a continuous-time system via impulsive input," Int. J. Bifurcation and Chaos 12, 1121-1128.
31. Yang, T. & Chua, L. O. [1997] "Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication," Int. J. Bifurcation and Chaos 7, 645-664.
32. Yang, T. & Chua, L. O. [2000] "Practical stability of impulsive synchronization between two nonautonomous chaotic systems," Int. J. Bifurcation and Chaos 10, 859-867.
33. Yang, W., Ding, M., Mandell, A. J. & Ott, E. [1995] "Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders," Phys. Rev. E51, 102-110.
34. Yuan, J., Gu, F. J. & Chai, Z. J. [2002] Methods and Applications of Neural Dynamics Models (Science Press, Beijing, China).
35. Zhang, H. & Quan, Y. [2001] "Modelling, identification and control of a class of nonlinear system," IEEE Trans. Fuzzy Syst. 9, 349-354.
36. Zhang, H., Wang, Z., Li, M., Quan, Y. & Zhang, M. [2004a] "Generalized fuzzy hyperbolic model: A universal approximator," ACTA Autom. Sin. 30, 416-422.
37. Zhang, H., Wang, Z. & Liu, D. [2004b] "Chaotifying fuzzy hyperbolic model using adaptive inverse optimal control approach," Int. J. Bifurcation and Chaos 14, 3505-3517.
38. Zhong, G. Q., Man, K. F. & Chen, G. [2001] "Generating chaos via a dynamical controller," Int. J. Bifurcation and Chaos 11, 865-869.