分数阶Newton-Leipnik混沌系统滑模同步的两种方法
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摘要
基于滑模控制及比例积分滑模控制,设计滑模函数和控制器,并给出分数阶NewtonLeipnik混沌系统取得同步的充分性条件.结果表明,若选取适当的控制律和滑模面,则分数阶Newton-Leipnik混沌系统的主从系统可取得滑模同步及比例积分滑模同步.
Based on sliding mode control and proportional integral sliding mode control,the author designed sliding mode functions and controller,and gave sufficient conditions for synchronization of fractional-order Newton-Leipnik chaotic systems.The results show that the master-slave systems of fractional-order Newton-Leipnik systems obtain sliding mode synchronization and proportional integral sliding mode synchronization if proper control law and sliding mode surfaces are selected.
Based on sliding mode control and proportional integral sliding mode control,the author designed sliding mode functions and controller,and gave sufficient conditions for synchronization of fractional-order Newton-Leipnik chaotic systems.The results show that the master-slave systems of fractional-order Newton-Leipnik systems obtain sliding mode synchronization and proportional integral sliding mode synchronization if proper control law and sliding mode surfaces are selected.
引文
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[16]徐瑞萍,高明美,刘振.一个新混沌系统的滑模控制[J].青岛大学学报(自然科学版),2012,25(3):26-29.(XU Ruiping,GAO Mingmei,LIU Zhen.Sliding Mode Control of a New Chaos System[J].Journal of Qingdao University(Natural Science Edition),2012,25(3):26-29.)
[17]胡建兵,赵灵冬.分数阶系统稳定性理论与控制研究[J].物理学报,2013,62(24):240504.(HU Jianbing,ZHAO Lingdong.Stability Theorem and Control of Fractional-Order Systems[J].Acta Phys Sin,2013,62(24):240504.)
[18]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用[M].北京:清华大学出版社,2003.(MEI Shengwei,SHEN Tielong,LIU Kangzhi.Modern Robust Control Theory and Application[M].Beijing:Tsinghua University Press,2003.)
[2]毛北行,李巧利.分数阶参数不确定系统的异结构混沌同步[J].中国海洋大学学报(自然科学版),2017,47(7):149-152.(MAO Beixing,LI Qiaoli.Chaos Synchronization between Different Fractional-Order Systems with Uncertain Parameters[J].Periodical of Ocean University of China,2017,47(7):149-152.)
[3]毛北行,孟晓玲.具有死区输入的分数阶多涡卷混沌系统的有限时间同步[J].浙江大学学报(理学版),2017,44(3):302-306.(MAO Beixing,MENG Xiaoling.Finite-Time Synchronization of Fractional-Order Multi-scroll Systems with Dead-Zone Input[J].Journal of Zhejiang University(Science Edition),2017,44(3):302-306.)
[4]王明军,王兴元.分数阶Newton-Leipnik系统的动力学分析[J].物理学报,2010,59(3):1583-1592.(WANG Mingjun,WANG Xingyuan.Dynamic Analysis of Fractional-Order Newton-Leipnik System[J].Acta Phys Sin,2010,59(3):1583-1592.)
[5]XIN Baogui,ZHANG Jinyi.Finite-Time Stabilizing a Fractional-Order Chaotic Financial System with Market Confidence[J].Nonlinear Dynamics,2015,79(2):1399-1409.
[6]Mohadeszadeh M,Delavari H.Synchronization of Fractional-Order Hyper-chaotic Systems Based on a New Adaptive Sliding Mode Control[J].Int J Dynam Control,2015,5(1):124-134.
[7]毛北行.两类分数阶系统的观测器同步[J].吉林大学学报(理学版),2017,55(1):139-144.(MAO Beixing.Observer Synchronization of Two Kinds of Fractional-Order Systems[J].Journal of Jilin University(Science Edition),2017,55(1):139-144.)
[8]SU Haipeng,LUO Runzi,ZENG Yanhui.The Exponential Synchronization of a Class of Fractional-Order Chaotic Systems with Discontinuous Input[J].Optik,2017,131:850-861.
[9]LUO Runzi,SU Haipeng,ZENG Yanhui.Synchronization of Uncertain Fractional-Order Chaotic Systems via a Novel Adaptive Controller[J].Chinese Journal of Physics,2017,55(2):342-349.
[10]孙宁,叶小岭,刘波.R9ssler混沌系统的自适应滑模控制[J].计算机仿真,2014,31(8):382-386.(SUN Ning,YE Xiaoling,LIU Bo.Adaptive Sliding Mode Control of R9ssler Chaotic System[J].Computer Simulations,2014,31(8):382-386.)
[11]毛北行,李巧利.一类分数阶Duffling-Van der pol系统的混沌同步[J].吉林大学学报(理学版),2016,54(2):369-373.(MAO Beixing,LI Qiaoli.Chaos Sychronization of a Class of Fractional-Order Duffling-Van der pol Systems[J].Journal of Jilin University(Science Edition),2016,54(2):369-373.)
[12]毛北行,李巧利.一类多涡卷系统的滑模有限时间混沌同步[J].吉林大学学报(理学版),2016,54(5):1131-1136.(MAO Beixing,LI Qiaoli.Finite-Time Sliding Mode Chaos Synchronization of a Kind of Multi-scroll Systems[J].Journal of Jilin University(Science Edition),2016,54(5):1131-1136.)
[13]徐瑞萍,高明美.自适应终端滑模控制不确定混沌系统的同步[J].控制工程,2016,23(5):715-719.(XU Ruiping,GAO Mingmei.Synchronization of Chaotic Systems with Uncertainty Using an Adaptive Terminal Sliding Mode Controller[J].Control Engineering of China,2016,23(5):715-719.)
[14]马珍珍,肖剑,杨叶红.一类具有二次项的新分数阶MAVPD混沌系统[J].武汉大学学报(工学版),2014,47(2):276-280.(MA Zhenzhen,XIAO Jian,YANG Yehong.A Type of Fractional-Order Chaotic Systems with Quadratic Term[J].Engineering Journal of Wuhan University,2014,47(2):276-280.)
[15]侯瑞茵,李俨,侯明善.比例积分追踪制导方法研究[J].西北工业大学学报,2014,32(2):303-308.(HOU Ruiyin,LI Yan,HOU Mingshan.A Proportional Plus Integral Pursuit Guidance Law[J].Journal of Northwestern Polytechnical University,2014,32(2):303-308.)
[16]徐瑞萍,高明美,刘振.一个新混沌系统的滑模控制[J].青岛大学学报(自然科学版),2012,25(3):26-29.(XU Ruiping,GAO Mingmei,LIU Zhen.Sliding Mode Control of a New Chaos System[J].Journal of Qingdao University(Natural Science Edition),2012,25(3):26-29.)
[17]胡建兵,赵灵冬.分数阶系统稳定性理论与控制研究[J].物理学报,2013,62(24):240504.(HU Jianbing,ZHAO Lingdong.Stability Theorem and Control of Fractional-Order Systems[J].Acta Phys Sin,2013,62(24):240504.)
[18]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用[M].北京:清华大学出版社,2003.(MEI Shengwei,SHEN Tielong,LIU Kangzhi.Modern Robust Control Theory and Application[M].Beijing:Tsinghua University Press,2003.)