Chaotic test of a 4-D non-equilibrium fractional order chaotic system and its control
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- 英文论文题名：Chaotic test of a 4-D non-equilibrium fractional order chaotic system and its control
- 论文作者：Keyong Shao ; Yeqiang Yu ; Jiahuan Sun ; Lipeng Zhou ; Jichi Wang ; Feng Chen
- 英文论文作者：Keyong Shao ; Yeqiang Yu ; Jiahuan Sun ; Lipeng Zhou ; Jichi Wang ; Feng Chen ; School of Electrical and Information Engineering Northeast Petroleum University ; Logging & Testing Services Company ; Daqing Oilfield Co.Ltd.
- 年：2017
- 作者机构：School of Electrical and Information Engineering Northeast Petroleum University;Logging & Testing Services Company,Daqing Oilfield Co.Ltd.;
- 英文论文关键词：4-D non-equilibrium fractional order chaotic system ; 0-1 test ; modification of the differential transform method ; qausi state feedback
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231;O415.5
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：602k
- 原文格式：D
- 会议级别：全国
摘要
A 4-D fractional order chaotic system without equilibrium point is studied in this paper, the modification of the differential transform method(MDTM) is applied to solving the fractional order chaotic system, and 0-1 test method is used to test chaotic of the system, the regular and chaotic motions can be decided by calculating the asymptotic growth rate K approaching asymptotically to zero or one. We give the stable condition for the stability of the system via qausi state feedback, and also design a qausi state feedback controller to stabilize the 4-D fractional order chaotic system. The feasibility of the algorithm is verified by simulation example.
A 4-D fractional order chaotic system without equilibrium point is studied in this paper, the modification of the differential transform method(MDTM) is applied to solving the fractional order chaotic system, and 0-1 test method is used to test chaotic of the system, the regular and chaotic motions can be decided by calculating the asymptotic growth rate K approaching asymptotically to zero or one. We give the stable condition for the stability of the system via qausi state feedback, and also design a qausi state feedback controller to stabilize the 4-D fractional order chaotic system. The feasibility of the algorithm is verified by simulation example.
A 4-D fractional order chaotic system without equilibrium point is studied in this paper, the modification of the differential transform method(MDTM) is applied to solving the fractional order chaotic system, and 0-1 test method is used to test chaotic of the system, the regular and chaotic motions can be decided by calculating the asymptotic growth rate K approaching asymptotically to zero or one. We give the stable condition for the stability of the system via qausi state feedback, and also design a qausi state feedback controller to stabilize the 4-D fractional order chaotic system. The feasibility of the algorithm is verified by simulation example.
引文
[1]Podlubny I,Fractional differential equations.New York:Academic Press,1999,chapter 2.
[2]Hifer R,Applications of fractional calculus in physics.New Jersey:World Scientific,2001,chapter 3.
[3]Ahmad WM,El-Khazali R,Fractional-order dynamical models of love,Chaos,Solitons and Fractals,2007,33(4):1367-1375.
[4]L JH,Han FL,Yu XH,Chen G,Generating 3-D multi-scroll chaotic attractors:a hysteresis series switching method,Automatica,2004,40(10):1677-1687.
[5]L JH,Chen G.Multi-scroll chaos generation:theories methods and applications,Int J Bifurc Chaos,2006,16(4):775-858.
[6]Habib D,Antonio L,Safya B,A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers,Commun Nonlinear Sci Numer Simul,2012,17(9):3727-3739.
[7]Yu S,Lu J,Yu X,Chen G,Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops,IEEE Trans CAS-I,2012,59(5):1015-1028.
[8]Li HQ,Liao XF,Luo MW,A novel non-equilibrium fractionalorder chaotic system and its complete synchronization by circuit implementation,Nonlinear Dyn,2012,68(68):137-149.
[9]Ping Zhou,Kun Huang,A new 4-D non-equilibrium fractionalorder chaotic system and its circuit implementation,Commun Nonlinear Sci Numer Simulat,2014,19(6):2005-2011.
[10]Zenghui Wang,Shijian Cang,Elisha Oketch Ochola,Yanxia Sun,A hyperchaotic system without equilibrium,Nonlinear Dyn,2012,69(1-2):531-537.
[11]Donato Cafagna,Giuseppe Grassi,Chaos in a new fractionalorder system without equilibrium points,Commun Nonlinear Sci Numer Simulat,2014,19(9):2919-2927.
[12]Ping Zhou,Fangyan Yang,Hyperchaos,chaos,and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points,Nonlinear Dyn,2014,76(1):473-480.
[13]Zhouchao Wei,Rongrong Wang,Anping Liu,A new finding of the existence of hidden hyperchaoticattractors with no equilibria.Mathematics and Computers in Simulation,2014,100(C):13-23.
[14]Yuming Chen,Qigui Yang,A new Lorenz-type hyperchaotic system with a curve of equilibria,Mathematics and Computers in Simulation,2015,112:40-55.
[15]Georg A.Gottwalda,Ian Melbourneb,Testing for chaos in deterministic systems with noise,Physica D,2004,212(212):100-110.
[16]Sun Ke-Hui,Liu Xuan,and Zhu Cong-Xu,The 0-1 test algorithm for chaos and its applications,Chin,Phys.B,2010,19(11):110510-7.
[17]G.Litak,A.Syta,M.Budhraja,L.M.Saha,Detection of the chaotic behaviour of a bouncing ball by the 0C1 test,Chaos,Solitons and Fractals,2009,42(3):1511-1517.
[18]Grzegorz Litak,Arkadiusz Syta,Marian Wiercigroch,Identification of chaos in a cutting process by the 0C1 test,Chaos,Solitons and Fractals,2009,40(5):2095-2101.
[19]Aytac Arikoglu,Ibrahim Ozkol,Solution of fractional differential equations by using differential transform method,Chaos,Solitons and Fractals,2007,34(5):1473-1481.
[20]Shaher Momani,Zaid Odibat,Vedat Suat Erturk,Generalized differential transform method for solving a spaceand timefractional diffusion-wave equation,Physics Letters A,2007,370(5):379-387.
[21]Z.Odibat,S.Momani,V.Erturk,Generalized differential transform method:application to differential equations of fractional order,Appl.Math.Comput.,2008,197(197):467-477.
[22]Jianbing Hu,Guoping Lu,Shibing Zhang,Lingdong Zhao,Lyapunov stability theorem about fractional system without and with delay,Commun Nonlinear Sci Numer Simulat,2015,20(3):905-913.
[23]Manuel A.Duarte-Mermoud,Norelys Aguila-Camacho,Javier A,Gallegos,Rafael Castro-Linares,Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,Commun Nonlinear Sci Numer Simulat,2014,22(1-4):650-659.
[24]Yan Li,Yang Quan Chen,Igor Podlubny,Stability of fractional-order nonlinear dynamic systems:Lyapunov direct method and generalized Mittag-Leffler stability,Computers and Mathematics with Applications,2010,59(5):1810-1821.
[25]Norelys Aguila-Camacho,Manuel A,Duarte-Mermoud,Javier A.Gallegos.Lyapunov functions for fractional order systems,Commun Nonlinear Sci Numer Simulat,2014,19(9):2951-2957.
[2]Hifer R,Applications of fractional calculus in physics.New Jersey:World Scientific,2001,chapter 3.
[3]Ahmad WM,El-Khazali R,Fractional-order dynamical models of love,Chaos,Solitons and Fractals,2007,33(4):1367-1375.
[4]L JH,Han FL,Yu XH,Chen G,Generating 3-D multi-scroll chaotic attractors:a hysteresis series switching method,Automatica,2004,40(10):1677-1687.
[5]L JH,Chen G.Multi-scroll chaos generation:theories methods and applications,Int J Bifurc Chaos,2006,16(4):775-858.
[6]Habib D,Antonio L,Safya B,A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers,Commun Nonlinear Sci Numer Simul,2012,17(9):3727-3739.
[7]Yu S,Lu J,Yu X,Chen G,Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops,IEEE Trans CAS-I,2012,59(5):1015-1028.
[8]Li HQ,Liao XF,Luo MW,A novel non-equilibrium fractionalorder chaotic system and its complete synchronization by circuit implementation,Nonlinear Dyn,2012,68(68):137-149.
[9]Ping Zhou,Kun Huang,A new 4-D non-equilibrium fractionalorder chaotic system and its circuit implementation,Commun Nonlinear Sci Numer Simulat,2014,19(6):2005-2011.
[10]Zenghui Wang,Shijian Cang,Elisha Oketch Ochola,Yanxia Sun,A hyperchaotic system without equilibrium,Nonlinear Dyn,2012,69(1-2):531-537.
[11]Donato Cafagna,Giuseppe Grassi,Chaos in a new fractionalorder system without equilibrium points,Commun Nonlinear Sci Numer Simulat,2014,19(9):2919-2927.
[12]Ping Zhou,Fangyan Yang,Hyperchaos,chaos,and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points,Nonlinear Dyn,2014,76(1):473-480.
[13]Zhouchao Wei,Rongrong Wang,Anping Liu,A new finding of the existence of hidden hyperchaoticattractors with no equilibria.Mathematics and Computers in Simulation,2014,100(C):13-23.
[14]Yuming Chen,Qigui Yang,A new Lorenz-type hyperchaotic system with a curve of equilibria,Mathematics and Computers in Simulation,2015,112:40-55.
[15]Georg A.Gottwalda,Ian Melbourneb,Testing for chaos in deterministic systems with noise,Physica D,2004,212(212):100-110.
[16]Sun Ke-Hui,Liu Xuan,and Zhu Cong-Xu,The 0-1 test algorithm for chaos and its applications,Chin,Phys.B,2010,19(11):110510-7.
[17]G.Litak,A.Syta,M.Budhraja,L.M.Saha,Detection of the chaotic behaviour of a bouncing ball by the 0C1 test,Chaos,Solitons and Fractals,2009,42(3):1511-1517.
[18]Grzegorz Litak,Arkadiusz Syta,Marian Wiercigroch,Identification of chaos in a cutting process by the 0C1 test,Chaos,Solitons and Fractals,2009,40(5):2095-2101.
[19]Aytac Arikoglu,Ibrahim Ozkol,Solution of fractional differential equations by using differential transform method,Chaos,Solitons and Fractals,2007,34(5):1473-1481.
[20]Shaher Momani,Zaid Odibat,Vedat Suat Erturk,Generalized differential transform method for solving a spaceand timefractional diffusion-wave equation,Physics Letters A,2007,370(5):379-387.
[21]Z.Odibat,S.Momani,V.Erturk,Generalized differential transform method:application to differential equations of fractional order,Appl.Math.Comput.,2008,197(197):467-477.
[22]Jianbing Hu,Guoping Lu,Shibing Zhang,Lingdong Zhao,Lyapunov stability theorem about fractional system without and with delay,Commun Nonlinear Sci Numer Simulat,2015,20(3):905-913.
[23]Manuel A.Duarte-Mermoud,Norelys Aguila-Camacho,Javier A,Gallegos,Rafael Castro-Linares,Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,Commun Nonlinear Sci Numer Simulat,2014,22(1-4):650-659.
[24]Yan Li,Yang Quan Chen,Igor Podlubny,Stability of fractional-order nonlinear dynamic systems:Lyapunov direct method and generalized Mittag-Leffler stability,Computers and Mathematics with Applications,2010,59(5):1810-1821.
[25]Norelys Aguila-Camacho,Manuel A,Duarte-Mermoud,Javier A.Gallegos.Lyapunov functions for fractional order systems,Commun Nonlinear Sci Numer Simulat,2014,19(9):2951-2957.