Synchronization of different-order chaotic systems: Adaptive active vs. optimal control

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 9, 2012, Pages 3643-3657

  Motallebzadeh, Foroogh ^a   Jahed Motlagh, Mohammad Reza ^a   Rahmani Cherati, Zahra ^b  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

^b BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Neural system; Nonlinear adaptive control; Optimal control; Reduced order synchronization

Indexed keywords

ADAPTIVE ALGORITHMS; ADAPTIVE CONTROL SYSTEMS; CHAOTIC SYSTEMS;

ADAPTIVE CONTROL STRATEGY; CONTROL MODULE; MODULARS; NEURAL SYSTEMS; NEURON MODELING; NONLINEAR ADAPTIVE CONTROL; OPTIMAL CONTROLS; REDUCED ORDER; REDUCED-ORDER SYNCHRONIZATION; SLAVE SYSTEMS;

SYNCHRONIZATION;

EID: 84859164258     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.01.012     Document Type: Article

References (39)

1. Ott E., Grebogi C., Yorke J.A. Controlling chaos. Phys Rev Lett 1990, 64:1196-1199.
2. Pecora L.M., Caroll T.L. Synchronization in chaotic systems. Phys Rev Lett 1990, 64:821-824.
3. Boccaletti S., Kurths J., Osipov G., Valladares D.L., Zhou C.S. The synchronization of chaotic systems. Phys Rep 2002, 366:1-101.
4. Rosenblum M.G., Pikovsky A.S., Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett 1996, 76:1804-1807.
5. Wang Q.Y., Lu Q.S., Duan Z.S. Adaptive lag synchronization in coupled chaotic systems with unidirectional delay feedback. Int J Nonlinear Mech 2010, 45:640-646.
6. Femat R., Solis-Perales G. On the chaos synchronization phenomena. Phys Lett A 1999, 262:50-60.
7. Yang T., Chua L.O. Generalized synchronization of chaos via linear transformations. Int J Bifurcat Chaos 1999, 9:215-219.
8. Nian F., Wang X. Chaotic synchronization of hybrid state on complex networks. Int J Mod Phys C 2010, 21:457-469.
9. Nian F., Wang X., Niu Y., Lin D. Module-phase synchronization in complex dynamic system. Appl Math Comput 2010, 217:2481-2489.
10. Terman D., Kopell N., Bose A. Dynamics of two mutually coupled slow inhibitory neurons. Physica D 1998, 117:241-275.
11. Schäfer C., Rosenblum M.G., Abel H.-H., Kurths J.R. Synchronization in the human cardiorespiratory system. Phys Rev E 1999, 60:857-870.
12. Femat R, Solís-Perales G. Synchronization of chaotic systems with different order. Phys Rev E 65 2002;(036226):1-7.
13. Laoye J.A., Vincent U.E., Akigbogun O.O. Chaos control and reduced-order synchronization of the rigid body. Int J Nonlinear Sci 2008, 6:106-113.
14. Ge Z.-M., Chang C.-M., Chen Y.-S. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems. Chaos Soliton Fract 2006, 27:1298-1315.
15. Rodríguez A., León J.D., Fridman L. Quasi-continuous high-order sliding-mode controllers for reduced-order chaos synchronization. Int J Nonlinear Mech 2008, 43:948-961.
16. Vincent U.E., Guo R. A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems. Commun Nonlinear Sci Numer Simulat 2009, 14:3925-3932.
17. Xu W., Yang X.L., Sun Z.K. Full- and reduced-order synchronization of a class of time-varying systems containing uncertainties. Nonlinear Dyn 2008, 52:19-25.
18. Krstic M., Kanellakopoulos I., Kokotovic P. Nonlinear and adaptive control design 1995, John Wiley & Sons, New York.
19. Yuen P.K., Baua H.H. Optimal and adaptive control of chaotic convection-theory and experiments. Phys Fluids 1999, 11:1435-1448.
20. Rafikov M., Balthazar J.M. On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun Nonlinear Sci Numer Simulat 2008, 13:1246-1255.
21. Tong C-F, Zhang H, Sun Y-X. Optimal control for a class of chaos synchronization with input constraint. In: proc. American Control Conference, Minneapolis, Minnesota, USA; 2006. p. 5282-5287.
22. El-Gohary A. Optimal synchronization of Rössler system with complete uncertain parameters. Chaos Soliton Fract 2006, 27:345-355.
23. Motallebzadeh F, Jahed Motlagh M, Rahmani Cherati Z. Reduced-order synchronization of chaotic systems: a modular adaptive design. In: IEEE International Conference on Control and Automation, Xiamen, China; 2010. p. 1595-1600.
24. Elson R.C., Selverston A.I., Huerta R., Rulkov N.F., Rabinovich M.I., Abarbanel H.D.I. Synchronous behavior of two coupled biological neurons. Phys Rev Lett 1998, 81:5692-5695.
25. Tass P., Haken H. Synchronized oscillations in the visual cortex - a synergetic model. Biol Cybern 1996, 74:31-39.
26. Kreiter A.K., Singer W. Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey. J Neurosci 1996, 16:2381-2396.
27. Harris-Warrick R.M., Marder E., Selverston A.I., Moulins M. Dynamic biological networks: the stomatogastric nervous system 1992, MIT, Cambridge.
28. Thompson CJ, Bardos DC, Yang YS, Joyner KH. Nonlinear cable models for cells exposed to electric fields I. general theory and space-clamped solutions, Chaos Soliton Fract 1999;10:1825-1842.
29. Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Physica D 1985, 16:285-317.
30. Hindmarsh JL, Rose RM. A model of neuronal bursting using three couple first order differential equations. In proc. of the Royal Society of London, Series B, Biological Sciences 1984;221:87-102.
31. Ioannou P., Fidden B. Adaptive control tutorial 2006, SIAM Press, Philadelphia.
32. Tao G. Adaptive control design and analysis 2003, John Wiley & Sons, New Jersey.
33. Bai E.-W., Lonngren K.E. Synchronization of two Lorenz systems using active control. Chaos Soliton Fract 1997, 8:51-58.
34. Kirk DE. Optimal Control Theory: an Introduction, Prentice Hall, Engelwood Cliffs, New Jersey, 1970.
35. Alasty A, Salarieh H. Identification and control of chaos using fuzzy clustering and sliding mode control in unmodeled affine dynamical systems, J Dyn Syst-T ASME 2008;130(011004):1-8.
36. Jiang W., Bin D., Tsang K.M. Chaotic synchronization of neurons coupled with gap junction under external electrical stimulation. Chaos Soliton Fract 2004, 22:469-476.
37. Suykens JAK, Curran PF, Vandewalle J, Chua LO. Robust nonlinear H∞ synchronization of chaotic Lur'e systems. In: IEEE Trans On Circ. and Syst. I 1997;44:891-904.
38. Moukam Kakmeni FM, Bowong S, Senthikumar DV, Kurths J. Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties, Chaos 2010;20:0431211-9.
39. Femat R., Alvarez-Ramirez J. Synchronization of a class of strictly different chaotic oscillators. Phys Lett A 1997, 236:307-313.