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Active disturbance rejection control of a chaotic system based on immune binary-state particle swarm optimization algorithm

Zhang Ying-Jie Wu Jian-Hui Zhang Jing Liu Zhao-Hua

Active disturbance rejection control of a chaotic system based on immune binary-state particle swarm optimization algorithm

Zhang Ying-Jie, Wu Jian-Hui, Zhang Jing, Liu Zhao-Hua
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  • The active disturbance rejection control (ADRC) has the property of requiring no knowledge about the precise mathematical model, but the parameters of controller is difficult to be tuned. An active disturbance rejection control based on immune binary-state particle swarm optimization algorithm (IBPSO-ADRC) is proposed, which takes advantage of the combination of the artificial immune systems (AIS) and particle swarm optimization (PSO). The proposed algorithm is applied to optimize the parameters of ADRC and then to control chaotic system. Furthermore, a new ADRC for the chaotic system is constructed. The simulation experiments indicate that the scheme requires no knowledge about the mathematical model with fast response speed, while restraining the parameter perturbation of chaotic system effectively and is robust to noise.
    • Funds:
    [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196

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    Hernault M L, Barbot J P, Ouslimani A 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 614

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    Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6121(in Chinese)[王永生、孙 瑾、王昌金、范洪达 2008 物理学报 57 6121]

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    Lu J Q, Cao J D, Daniel W C H 2008 IEEE Trans. Circ. Syst. (Part I) 55 1347

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    Alexander L F, Boris A, Robin J E 2008 IEEE Trans. Circ. Syst. 55 1685

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    Lam H K, Ling W K, Iu H C H, Ling S H S 2008 IEEE Trans. Circ. Syst. 55 893

    [8]

    Wang X Y, Meng J 2009 Acta. Phys. Sin. 58 3780 (in chinese)[王兴元、孟 娟 2009.物理学报 58 3780]

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    Wang D F, Han P 2006 Acta. Phys. Sin. 55 1644(in Chinese)[王东风、韩 璞 2006 物理学报 55 1644]

    [10]

    Liu H, Liu D 2007 Control Theory & Applications 24 761(in Chinese)[刘 涵、刘 丁 2007 控制理论与应用 24 761]

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    Han J Q 2009 IEEE Trans.Industrial Electronics 56 900

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    Han J Q2008 Active Disturbance Rejection Control Technique (Beijing: National Defense Industry Press) p2(in Chinese)[韩京清 2008 自抗扰控制技术 (北京: 国防工业出版社) 第2页]

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    ZhangW G, Han J Q2000 Control and Decision 15 301(in Chinese)[张文革、韩京清 2000 控制与决策 15 301]

    [14]

    Shao L W, Liao X Z, Zhang Y H 2008 Control Theory & Applications 25 205[邵立伟、廖晓钟、张宇河 2008 控制理论与应用 25 205]

    [15]

    Shi Y L, Hou C Z, Su H B 2008 Journal of System Simulation 20 433(in Chinese)[史永丽、侯朝桢、苏海滨 2008 系统仿真学报 20 433]

    [16]

    Xin J, Liu D, Yang Y X 2007 Control Theory & Applications 24 546 (in chinese)[辛 菁、刘 丁、杨延西 2007 控制理论与应用 24 546]

    [17]

    Eberchart R, Kennedy J 1995 Proc. Int. Sym. Micro Machine and Human Science(Nagoya Japan IEEE Press)p39

    [18]

    Li X D, Engelbrecht A. P 2007 Proc. Genetic Evol. Comput.Conf (London, United Kingdom),July 07—11 2007 p3391

    [19]

    Zhan Z H, Zhang J, Li Y, Chung H S H 2009 IEEE Trans. Syst. Man. Cyber (Part B) 39 1362

    [20]

    DeCastro L N, VonZuben F J 2002 IEEE Trans. Evol. Comp. 62 39

    [21]

    Ge H W, Sun L, Liang Y C, Qian F 2008 IEEE Trans. Syst. Man. Cyber (Part A) 38 358

    [22]

    Liu J K 2007 Advanced PID control and MATLAB Simulation (Beijing: Eleectrical Industry Press) P163, p263(in Chinese)[刘金琨 2007 先进PID控制MATLAB仿真 (北京: 电子工业出版社) 第163, 263页]

    [23]

    Hou Z S, Wang W H, Jin S T 2009 Control Theory & Applications 26 505(in Chinese)[侯忠生、王卫红、金尚泰 2009 控制理论与应用 26 509]

    [24]

    Wen S H, Wang Z, Liu F C 2009 Acta. Phys. Sin. 58 3753(in Chinese)[温淑焕、王 哲、刘福才 2009 物理学报 58 3753]

  • [1]

    Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196

    [2]

    Hernault M L, Barbot J P, Ouslimani A 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 614

    [3]

    Li Z G, Li K, Wen C G, Soh Y C 2003 IEEE Trans. Comm. 51 1306

    [4]

    Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6121(in Chinese)[王永生、孙 瑾、王昌金、范洪达 2008 物理学报 57 6121]

    [5]

    Lu J Q, Cao J D, Daniel W C H 2008 IEEE Trans. Circ. Syst. (Part I) 55 1347

    [6]

    Alexander L F, Boris A, Robin J E 2008 IEEE Trans. Circ. Syst. 55 1685

    [7]

    Lam H K, Ling W K, Iu H C H, Ling S H S 2008 IEEE Trans. Circ. Syst. 55 893

    [8]

    Wang X Y, Meng J 2009 Acta. Phys. Sin. 58 3780 (in chinese)[王兴元、孟 娟 2009.物理学报 58 3780]

    [9]

    Wang D F, Han P 2006 Acta. Phys. Sin. 55 1644(in Chinese)[王东风、韩 璞 2006 物理学报 55 1644]

    [10]

    Liu H, Liu D 2007 Control Theory & Applications 24 761(in Chinese)[刘 涵、刘 丁 2007 控制理论与应用 24 761]

    [11]

    Han J Q 2009 IEEE Trans.Industrial Electronics 56 900

    [12]

    Han J Q2008 Active Disturbance Rejection Control Technique (Beijing: National Defense Industry Press) p2(in Chinese)[韩京清 2008 自抗扰控制技术 (北京: 国防工业出版社) 第2页]

    [13]

    ZhangW G, Han J Q2000 Control and Decision 15 301(in Chinese)[张文革、韩京清 2000 控制与决策 15 301]

    [14]

    Shao L W, Liao X Z, Zhang Y H 2008 Control Theory & Applications 25 205[邵立伟、廖晓钟、张宇河 2008 控制理论与应用 25 205]

    [15]

    Shi Y L, Hou C Z, Su H B 2008 Journal of System Simulation 20 433(in Chinese)[史永丽、侯朝桢、苏海滨 2008 系统仿真学报 20 433]

    [16]

    Xin J, Liu D, Yang Y X 2007 Control Theory & Applications 24 546 (in chinese)[辛 菁、刘 丁、杨延西 2007 控制理论与应用 24 546]

    [17]

    Eberchart R, Kennedy J 1995 Proc. Int. Sym. Micro Machine and Human Science(Nagoya Japan IEEE Press)p39

    [18]

    Li X D, Engelbrecht A. P 2007 Proc. Genetic Evol. Comput.Conf (London, United Kingdom),July 07—11 2007 p3391

    [19]

    Zhan Z H, Zhang J, Li Y, Chung H S H 2009 IEEE Trans. Syst. Man. Cyber (Part B) 39 1362

    [20]

    DeCastro L N, VonZuben F J 2002 IEEE Trans. Evol. Comp. 62 39

    [21]

    Ge H W, Sun L, Liang Y C, Qian F 2008 IEEE Trans. Syst. Man. Cyber (Part A) 38 358

    [22]

    Liu J K 2007 Advanced PID control and MATLAB Simulation (Beijing: Eleectrical Industry Press) P163, p263(in Chinese)[刘金琨 2007 先进PID控制MATLAB仿真 (北京: 电子工业出版社) 第163, 263页]

    [23]

    Hou Z S, Wang W H, Jin S T 2009 Control Theory & Applications 26 505(in Chinese)[侯忠生、王卫红、金尚泰 2009 控制理论与应用 26 509]

    [24]

    Wen S H, Wang Z, Liu F C 2009 Acta. Phys. Sin. 58 3753(in Chinese)[温淑焕、王 哲、刘福才 2009 物理学报 58 3753]

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    [6] Yu Ling-Hui, Liu Xiao-Jing, Gao Mei-Jing, Wu Shi-Chang, Lu Zhi-Gang. . Acta Physica Sinica, 2002, 51(10): 2211-2215. doi: 10.7498/aps.51.2211
    [7] Zhang Ling-Mei, Zhang Jian-Wen, Wu Run-Heng. Anti-control of Hopf bifurcation in the new chaotic system with piecewise system and exponential system. Acta Physica Sinica, 2014, 63(16): 160505. doi: 10.7498/aps.63.160505
    [8] Luo Run-Zi. Impulsive control and synchronization of a new chaotic system. Acta Physica Sinica, 2007, 56(10): 5655-5660. doi: 10.7498/aps.56.5655
    [9] Song Yun-Zhong, Li Wen-Lin. Chaos anti-control of nonlinear system with uncertainties. Acta Physica Sinica, 2008, 57(1): 51-55. doi: 10.7498/aps.57.51
    [10] Cao Xiao-Qun. Optimal control for a chaotic system by means of Gauss pseudospectral method. Acta Physica Sinica, 2013, 62(23): 230505. doi: 10.7498/aps.62.230505
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  • Received Date:  24 November 2009
  • Accepted Date:  16 April 2010
  • Published Online:  15 January 2011

Active disturbance rejection control of a chaotic system based on immune binary-state particle swarm optimization algorithm

  • 1. (1)College of Computer and Communication, Hunan University, Changsha 410082, China; (2)College of Electrical and Information Engineering, Hunan University, Changsha 410082, China; (3)College of Electrical and Information Engineering, Hunan University, Changsha 410082, China;College of Computer and Communication, Hunan University, Changsha 410082, China

Abstract: The active disturbance rejection control (ADRC) has the property of requiring no knowledge about the precise mathematical model, but the parameters of controller is difficult to be tuned. An active disturbance rejection control based on immune binary-state particle swarm optimization algorithm (IBPSO-ADRC) is proposed, which takes advantage of the combination of the artificial immune systems (AIS) and particle swarm optimization (PSO). The proposed algorithm is applied to optimize the parameters of ADRC and then to control chaotic system. Furthermore, a new ADRC for the chaotic system is constructed. The simulation experiments indicate that the scheme requires no knowledge about the mathematical model with fast response speed, while restraining the parameter perturbation of chaotic system effectively and is robust to noise.

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