Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

doi:10.1088/1674-1056/21/6/060506

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 60506-060506.doi: 10.1088/1674-1056/21/6/060506

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

Mohammad Pourmahmood Aghababa^a, Hassan Feizi^b

a. Electrical Engineering Department, Urmia University of Technology, Urmia, Iran;
b. Department of Mathematics, Mamaghan Branch, Islamic Azad University, Mamaghan, Iran

收稿日期:2011-07-24 修回日期:2011-11-04 出版日期:2012-05-01 发布日期:2012-05-01

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

Mohammad Pourmahmood Aghababa^a)† and Hassan Feizi^b)

a. Electrical Engineering Department, Urmia University of Technology, Urmia, Iran;
b. Department of Mathematics, Mamaghan Branch, Islamic Azad University, Mamaghan, Iran

Received:2011-07-24 Revised:2011-11-04 Online:2012-05-01 Published:2012-05-01
Contact: Mohammad Pourmahmood Aghababa E-mail:m.p.aghababa@ee.uut.ac.ir

摘要/Abstract

摘要： This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master's and the slave's system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

关键词: nonsingular terminal sliding mode, finite-time synchronization, uncertain parameter, nonlinear input

Abstract: This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master's and the slave's system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

Key words: nonsingular terminal sliding mode, finite-time synchronization, uncertain parameter, nonlinear input

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.-a (Nonlinear dynamics and chaos)

Mohammad Pourmahmood Aghababa, Hassan Feizi. Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs[J]. 中国物理B, 2012, 21(6): 60506-060506.

Mohammad Pourmahmood Aghababa and Hassan Feizi . Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs[J]. Chin. Phys. B, 2012, 21(6): 60506-060506.

参考文献 38

[1]	Pourmahmood M Khanmohammadi S Alizadeh G 2011 Commun. Nonlinear Sci. Numer. Simul. 16 2853
[2]	Aghababa M P Heydari A 2011 Appl. Math. Model. doi:10.1016/j.apm.2011.09.023
[3]	Aghababa M P 2011 Chin. Phys. B 20 090505
[4]	L? L, Li G, Guo L, Meng L, Zou J R and Yang M 2010 Chin. Phys. B 19 080507
[5]	Liu Y Z, Jiang C S, Lin C S and Jiang Y M 2007 Chin. Phys. 16 660
[6]	Wang B and Wen G 2007 Phys. Lett. A 370 35
[7]	Li G H, Zhou S P and Xu D M 2004 Chin. Phys. 13 168
[8]	Chen F X and Zhang W D 2007 Chin. Phys. 16 937
[9]	Zhang X Y, Guan X P and Li H G 2005 Chin. Phys. 14 279
[10]	Hu J and Zhang Q J 2008 Chin. Phys. B 17 503
[11]	Chen Y, Wu X and Gui Z 2010 Appl. Math. Model. 34 4161
[12]	Huang J 2008 Nonlinear Anal. 69 4174
[13]	Zhang G, Liu Z and Zhang J 2008 Phys. Lett. A 372 447
[14]	Zhang H, Huang W, Wang Z and Chai T 2006 Phys. Lett. A 350 363
[15]	Chen X and Lu J 2007 Phys. Lett. A 364 123
[16]	Shi X R and Wang Z L 2009 Appl. Math. Comput. 215 1711
[17]	Yang C 2010 Appl. Math. Comput. 216 1316
[18]	Zhou X, Wu Y, Li Y and Xue H 2008 Appl. Math. Comput. 203 80
[19]	Zhu C 2009 Appl. Math. Comput. 215 557
[20]	Chen Y H, Wang R R and Chang C 2010 Phys. Lett. A 374 2254
[21]	Ma J, Zhang A, Xia Y and Zhang L 2010 Appl. Math. Comput. 215 3318
[22]	Wu X, Guan Z, Wu Z and Li T 2007 Phys. Lett. A 364 484
[23]	Sharma B B and Kar I N 2009 Chaos, Solitons and Fractals 41 2437
[24]	Hwang E, Hyun C, Kim E and Park M 2009 Phys. Lett. A 373 1935
[25]	Zhang L, Huang L, Zhang Z and Wang Z 2008 Phys. Lett. A 372 6082
[26]	Yau H and Yan J 2008 Appl. Math. Comput. 197 775
[27]	Kebriaei H and Yazdanpanah M J 2010 Commun. Nonlinear Sci. Numer. Simul. 15 430
[28]	Yan J, Lin J and Liao T 2008 Chaos, Solitons and Fractals 36 45
[29]	Li W and Chang K 2009 Chaos, Solitons and Fractals 39 2086
[30]	Lin J, Yan J and Liao T 2005 Chaos, Solitons and Fractals 24 371
[31]	Ahn C K, Jung S, Kang S and Joo S 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2168
[32]	Jianwen F, Ling H, Chen X, Austin F and Geng W 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2546
[33]	Li S and Tian Y 2003 Chaos, Solitons and Fractals 15 303
[34]	Wang H, Han Z, Xie Q and Zhang W 2009 Nonlinear Anal. RWA 10 2842
[35]	Wang H, Han Z, Xie Q and Zhang W 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2239
[36]	Aghababa M P, Khanmohammadi S and Alizadeh G 2011 Appl. Math. Model. 35 3080
[37]	Bhat S P and Bernstein D S 2000 SIAM J. Control Optim. 38 751
[38]	Utkin V I 1992 Sliding Modes in Control Optimization (Berlin: Springer-Verlag)

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

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