Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

doi:10.1088/1674-1056/22/6/060508

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60508-060508.doi: 10.1088/1674-1056/22/6/060508

Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

Gamal M. Mahmoud^a, Emad E. Mahmoud^{b c}, Ayman A. Arafa^b

a Department of Mathematics, Faculty of Science, Taibah University, Al-Madeenah Al-Munawwarah, P. O. Box 344, Kingdom of Saudi Arabia;
b Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt;
c College of Applied Medical Sciences, Turabah, Taif University, Kingdom of Saudi Arabia

收稿日期:2012-10-07 修回日期:2012-12-16 出版日期:2013-05-01 发布日期:2013-05-01

Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

Gamal M. Mahmoud^a, Emad E. Mahmoud^{b c}, Ayman A. Arafa^b

a Department of Mathematics, Faculty of Science, Taibah University, Al-Madeenah Al-Munawwarah, P. O. Box 344, Kingdom of Saudi Arabia;
b Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt;
c College of Applied Medical Sciences, Turabah, Taif University, Kingdom of Saudi Arabia

Received:2012-10-07 Revised:2012-12-16 Online:2013-05-01 Published:2013-05-01
Contact: Gamal M. Mahmoud, Emad E. Mahmoud E-mail:gmahmoud@, aun.edu.eg, gmahmoud_56@yahoo.com; emad_eluan@yahoo.com

摘要/Abstract

摘要： The aim of this paper is to study the control of hyperchaotic complex nonlinear systems with unknown parameters using passive control theory. An approach is stated to design the passive controller and estimate the unknown parameters based on the property of the passive system. The feasibility and effectiveness of the proposed approach is demonstrated through its application to the hyperchaotic complex Lü system, as an example. The estimated values of the unknown parameters are calculated. The analytical form of the complex controller is derived and used in the numerical simulation to control the hyperchaotic attractors of this example. Block diagrams of this example using Matlab/Simulink are constructed after and before the control to ensure the validity of the analytical results. Other examples of hyperchaotic complex nonlinear systems can be similarly treated.

关键词: control, passive control, hyperchaotic, complex

Abstract: The aim of this paper is to study the control of hyperchaotic complex nonlinear systems with unknown parameters using passive control theory. An approach is stated to design the passive controller and estimate the unknown parameters based on the property of the passive system. The feasibility and effectiveness of the proposed approach is demonstrated through its application to the hyperchaotic complex Lü system, as an example. The estimated values of the unknown parameters are calculated. The analytical form of the complex controller is derived and used in the numerical simulation to control the hyperchaotic attractors of this example. Block diagrams of this example using Matlab/Simulink are constructed after and before the control to ensure the validity of the analytical results. Other examples of hyperchaotic complex nonlinear systems can be similarly treated.

Key words: control, passive control, hyperchaotic, complex

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Gg (Control of chaos, applications of chaos) 05.45.Xt (Synchronization; coupled oscillators)

Gamal M. Mahmoud, Emad E. Mahmoud, Ayman A. Arafa. Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method[J]. 中国物理B, 2013, 22(6): 60508-060508.

Gamal M. Mahmoud, Emad E. Mahmoud, Ayman A. Arafa. Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method[J]. Chin. Phys. B, 2013, 22(6): 60508-060508.

参考文献 51

[1]	Vidyasagar M 1979 IEEE Trans. Autom. Control 24 575
[2]	Willems J C 1972 Arch. Ration. Mech. Anal. 45 321
[3]	Lou X Y and Cui B T 2007 Neurocomputing 70 1071
[4]	Mahmoud G M, Mahmoud E E and Arafa A A 2012 J. Vib. Control
[5]	Xie L, Fu M and Li H 1998 IEEE Trans. Signal Process. 46 2394
[6]	Pogromsky A Y 1998 Int. J. Bifur. Chaos 8 295
[7]	Wang F Q and Liu C X 2007 Int. J. Mod. Phys. B 21 3053
[8]	Calcev G 1998 Autom. 33 339
[9]	Wen Y 1999 IEEE Trans. Circuits Syst. I 46 876
[10]	Byrnes C I, Isidori A and Willems J C 1991 IEEE Trans. Auto. Control 36 1228
[11]	Wang X J, Li J S and Chen G R 2008 Nonlinear Dyn. 53 45
[12]	Wei D Q and Luo X 2008 Chin. Phys. B 17 92
[13]	Kemih K 2009 Chaos, Solitons and Fractals 41 1897
[14]	Chen X and Liu C 2010 Nonlinear Analysis: Real World Applications 11 683
[15]	Sangpet T and Kuntanapreeda S 2010 Int. J. Bifur. Chaos 20 1519
[16]	Wang F and Liu C 2007 Physica D 225 55
[17]	Mahmoud E E 2012 J. Frank. Inst. 349 1247
[18]	Wei D Q, Zhang B and Luo X S 2012 Chin. Phys. B 21 030504
[19]	Fu S H, Lu Q S and Du Y 2012 Chin. Phys. B 21 060507
[20]	Zhu D R, Liu C X and Yan B N 2012 Chin. Phys. B 21 090509
[21]	Sangpet T and Kuntanapreeda S 2010 J. Sound Vib. 329 2490
[22]	Wei D Q, Luo X S, Zhang B and Qin Y H 2010 Nonlinear Analysis: Real World Applications 11 1752
[23]	Seron M M, Hill D J and Fradkov A L 1995 Autom. 31 1053
[24]	Yuan F G and Shen L Z 2010 Chin. Phys. B 19 060505
[25]	Jiang Z P, Hill D J and Fradkov A L 1996 Syst. Control Lett. 28 73
[26]	Wei W, Li D H and Wang J 2011 Chin. Phys. B 20 040510
[27]	Dai H, Jia L X, Hui M and Si G Q 2011 Chin. Phys. B 20 040507
[28]	Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[29]	Li C L, Yu S M and Luo X S 2012 Chin. Phys. B 21 100506
[30]	Niu Y J, Wang X Y and Pei B N 2012 Chin. Phys. B 21 030503
[31]	Mahmoud E E and Mahmoud G M 2010 On Some Chaotic Complex Nonlinear Systmes (Berlin: Lambert Academic Publishing)
[32]	Mahmoud E E and Mahmoud G M 2011 Chaotic and Hyperchaotic Nonlinear Systems (Berlin: Lambert Academic Publishing)
[33]	Mahmoud G M, Bountis T and Mahmoud E E 2007 Int. J. Bifur. Chaos 17 4295
[34]	Mahmoud G M and Mahmoud E E 2010 Nonlinear Dyn. 61 141
[35]	Mahmoud G M and Mahmoud E E 2010 Math. Comp. Simul. 80 2286
[36]	Mahmoud G M, Ahmed M E and Mahmoud E E 2008 Int. J. Mod. Phys. C 19 1477
[37]	Mahmoud G M, Mahmoud E E and Ahmed M E 2009 Nonlinear Dyn. 58 725
[38]	Mahmoud G M, Mahmoud E E and Ahmed M E 2007 Int. J. Appl. Math. Stat. 12 90
[39]	Mahmoud G M and Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[40]	Mahmoud G M, Bountis T, AbdEl-Latif G M and Mahmoud E E 2009 Nonlinear Dyn. 55 43
[41]	Mahmoud G M and Mahmoud E E 2010 Nonlinear Dyn. 62 875
[42]	Mahmoud G M and Mahmoud E E 2011 Int. J. Bifur. Chaos 21 2369
[43]	Mahmoud E E 2012 Math. Comp. Modelling 55 1951
[44]	Ning C Z and Haken H 1990 Phys. Rev. A 41 3827
[45]	Fowler A C, Gibbon J D and Mc Guinnes M T 1983 Physica D 7 126
[46]	Liu P and Liu S 2010 Nonlinear Analysis: Real World Applications 12 3046
[47]	Gibbon J D and Mc Guinnes M J 1982 Physica D 5 108
[48]	Nayfeh A H and Balachandran B 1995 Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (New York: Wiley)
[49]	Isidori A 1989 Nonlinear Control Systems (Berlin: Springer-Verlag)
[50]	Byrnes C I and Isidori A 1988 Syst. Control Lett. 11 9
[51]	Beucher O and Weeks M 2006 Introduction to Matlab and Simulink (München: Pearson Education Deutschland GmbH)

Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

Controlling hyperchaotic complex systems with unknown parameters based on adaptive passive method

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