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- 2018
纠缠混沌系统的比例积分滑模同步
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Abstract:
摘要： 基于滑模控制研究纠缠混沌系统的滑模同步与比例积分滑模同步,利用滑模及比例积分滑模方法设计滑模面和控制器,采用滑模等速趋近律,根据Lyapunov稳定性理论对系统轨线在滑模面及不在滑模面运动两种情形进行分析,在设计的滑模面和控制器的共同作用下可使误差系统在有限时间内趋近于坐标原点,得到系统取得滑模同步和积分滑模同步的两个充分条件。研究表明:选取适当的控制器与滑模面,纠缠混沌系统的主从系统取得滑模同步和积分滑模同步。
Abstract: The problem of sliding mode and ratio integral sliding mode synchronization of a class of entanglement chaotic systems were studied based on sliding mode control in the paper. The surfaces and controllers were designed using sliding mode and ratio integral sliding mode approach. And sliding mode uniform speed reaching law was adopted.Two cases for system trajectory on sliding mode surface and not on sliding mode surface were analyzed based on Lyapunov stability theory.The systems errors could approach to coordinate zero under the corporate action of surfaces and controllers. Two sufficient conditions were arrived for entanglement chaotic systems acquire sliding mode synchronization and integral sliding mode synchronization.The research conclusion illustrated that the master-slave systems of entanglement chaotic systems were sliding mode and ratio integral sliding mode synchronization if proper controllers and sliding mode surfaces was chosen
| [1] | 毛北行, 程春蕊. 分数阶Victor-Carmen混沌系统的自适应滑模控制[J]. 山东大学学报(工学版), 2017, 47(4):31-36. MAO Beixing, CHENG Chunrui. Self-adaptive sliding mode control of fractional-order Victor-Carmen chaotic systems[J]. Journal of Shandong University(Engineering Science), 2017, 47(4):31-36. |
| [2] | BHAT S P, BERNATEIN D S. Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control Signals and Systems, 2005, 17(2):101-127. |
| [3] | MOHAMMAD P A, SOHRAB K, GHASSEM A. Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique[J]. Applied Mathematical Modelling, 2011, 35(6):3080-3091. |
| [4] | 毛北行,王东晓. 分数阶多涡卷系统滑模控制混沌同步[J]. 山东大学学报(工学版),2017,47(3):79-83. MAO Beixing, WANG Dongxiao. Sliding mode chaos synchronization control of a class of fractional-order multi-scroll systems[J]. Journal of Shandong University(Engineering Science), 2017, 47(3):79-83. |
| [5] | 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. |
| [6] | AHMAD W, ELKHAZALI R. Fractional-order dynamical models of love[J]. Chaos Soliton Fract, 2007, 33(4):1367-1375. |
| [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] | MOHAMMAD P A. Robust finite-time stabilization of fractional-order chaotic susyems based on fractional Lyapunov stability theory[J]. Journal of Computation and Nonlinear Dynamics, 2012, 32(7):1011-1015. |
| [9] | 仲启龙, 邵永辉, 郑永爱. 分数阶混沌系统的主动滑模同步[J]. 动力学与控制学报, 2015, 13(1):18-22. ZHONG Qilong, SHAO Yonghui, ZHENG Yongai. Forwardly sliding mode synchronization of the fractional order chaotic systems[J]. Journal of Dynamics and Control, 2015, 13(1):18-22. |
| [10] | 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 susyems with uncertainty using adaptive terminal sliding mode controller[J]. Control Engineering of China, 2016, 23(5):715-719. |
| [11] | 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. |
| [12] | ZHANG H T, LIU X Z. Chaos entanglement:a new approach to generate chaos[J]. International Journal of Bifurcation and Chaos, 2013, 23(5):1330-1411. |
| [13] | 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 betweendifferen fractional-order systems with uncertain parameters[J]. Periodical of Ocean University of China, 2017, 47(7):149-152. |
| [14] | 张燕兰. 分数阶Rayleigh-Duffling-like系统的自适应追踪广义投影同步[J]. 动力学与控制学报, 2014, 12(4):348-352. ZHANG Yanlan. Adaptive tracking generalized projective synchronization of fractional Rayleigh-Duffling-like system[J]. Journal of Dynamics and Control, 2014, 12(4):348-352. |
| [15] | 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):276-285. 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):276-285. |
| [16] | 徐瑞萍, 高明美, 刘振. 一个系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] | 刘恒, 余海军, 向伟. 带有未知扰动的多涡卷混沌系统修正函数时滞投影同步[J]. 物理学报, 2012, 61(18):5031-5036. LIU Heng, YU Haijun, XIANG Wei. Modified function projective lag synchronization for multi-scroll chaotic system with unknown disturbances[J]. Acta Physica Sinica, 2012, 61(18):5031-5036. |
| [18] | MILAD Mohadeszadeh, HADI Delavari. Synchronization of fractional order hyper-chaotic systems based on a new adaptive sliding mode control[J]. International Journal Dynam Control, 2015, 10(7):435-446. |
| [19] | 杨敏, 俞建宁, 张建刚, 等. 一个新构造混沌纠缠系统的动力学分析[J]. 山东理工大学学报(自然科学版), 2014, 28(1):16-23. YANG Min, YU Jianning, ZHANG Jiangang, et al. Dynamical analysis of a new chaos entanglement system[J]. Journal of Shandong University of Technology(Natural Science Edition), 2014, 28(10):16-23. |
| [20] | 梅生伟, 申铁龙, 刘志康. 现代鲁棒控制理论与应用[M]. 北京清华大学出版社, 2003. |
