含对数项分数阶T混沌系统的滑模同步

doi:10.6040/j.issn.1672-3961.0.2019.395

摘要/Abstract

摘要： 利用Barbalat引理、分数阶稳定性理论,通过构造合适的分数阶线性滑模面和分数阶比例积分滑模面,设计合理的控制器,实现整数阶、分数阶T混沌系统滑模同步控制。研究结果表明:一定条件下,分数阶T混沌系统的驱动-响应系统能够达到滑模同步,用Matlab数值仿真验证了结论的正确性。

关键词: 分数阶, T混沌系统, 滑模同步, Barbalat引理, 滑模面

Abstract: By using the Barbalat lemma and fractional-order stability theory, and constructing proper fractional-order sliding mode surface and fractional-order proportion integral sliding mode surface, the controllers were designed to realize the synchronization control of integer model and fractional-order T chaotic systems. The research conclusion illustrated that the derive-responsive systems of fractional-order T chaotic systems could get sliding mode synchronization under certain conditions. MATLAB numerical simulation proved the correctness of the conclusions.

Key words: fractional-order, T chaotic system, sliding mode synchronization, Barbalat lemma, sliding surface

中图分类号:

O482.4

孟晓玲,毛北行. 含对数项分数阶T混沌系统的滑模同步[J]. 山东大学学报 (工学版), 2020, 50(5): 7-12.

MENG Xiaoling, MAO Beixing. Sliding mode synchronization of fractional-order T chaotic systems with logarithmic[J]. Journal of Shandong University(Engineering Science), 2020, 50(5): 7-12.

参考文献

[1] 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 adaptive terminal sliding mode controller[J]. Control Engineering, 2016, 23(5):715-719.
[2] 李鹏, 郑志强. 非线性积分滑模方法[J].控制理论与应用, 2011, 28(3):421-426. LI Peng, ZHENG Zhiqiang. Sliding mode control approach with nonlinear integrator[J]. Control Theory and Applications,2011,28(3):421-426.
[3] 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 Poly Technical University, 2014, 32(2):303-308.
[4] MOHAMMAD P A. Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov Stability Theory[J]. Journal of Computation and Nonlinear Dynamics, 2012, 7:1011-1015.
[5] MILAD Mo Hades Zadeh, HADI Delavari. Synchronization of fractional order hyper-chaotic systems based on a new adaptive sliding mode control[J]. Int J Dynam Control, 2015, 10(7):435-446.
[6] BHAT S P, BERNSTEIN D S. Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control Signals and Systems, 2005, 17(2):101-127.
[7] LI L, LI W, KURTHS J, et al. Pinning adaptive synchronization of a class of uncertain complex dynamical network with multi-link against network deterioration[J]. Chaos Solitons & Fractals, 2015, 72:20-34.
[8] CHAI Y, CHEN L, WU R, et al. Adaptive pinning synchronization in fractional-order complex dynamical networks[J]. Timing and Time Perception, 2015, 391(1/2):5746-5758.
[9] WANG X, HE Y. Projective synchronization of fractional order chaotic system based on linear separation[J]. Phys Lett A, 2008, 37:435-441.
[10] 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.
[11] 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.
[12] 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 Baoxing, LI Qiaoli. Chaos synchronization between different fractional-order systems with uncertain parameters[J]. Periodical of Ocean University of China, 2017, 47(7):149-152.
[13] 马广富, 于彦波, 李波, 等. 基于积分滑模的航天器有限时间姿态容错控制[J]. 控制理论与应用, 2017, 34(8):1028-1034. MA Guangfu, YU Yanbo, LI Bo, et al. Integral-type sliding mode finite-time fault tolerant control for spacecraft attitude control[J]. Control Theory Applications, 2017, 34(8):1028-1034.
[14] 赵斌,周军,卢晓东,等.考虑终端角度约束的自适应积分滑模制导律[J].控制与决策,2017, 32(11): 1966-1972. ZHAO Bin, ZHOU Jun, LU Xiaodong, et al. Adaptive integral sliding mode guidance law considering impact angel constraint[J]. Control and Decision, 2017, 32(11):1966-1972.
[15] 孙宁, 叶小岭, 刘波. Rössler 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 Rössler chaotic system[J]. Computer Simulations, 2014, 31(8):382-386.
[16] TIGAN G. Analysis of a 3D chaotic system [J]. Chaos, Solitons and Fractals, 2008(36):1315-1319.
[17] 王震,孙卫. T混沌系统的动力学分析及电路仿真[J].物理学报,2013,62(2):154-160. WANG Zhen, SUN Wei. Dynamical analysis and circuit simulation of T chaotic systems[J]. Physical Science Journal, 2013,62(2):154-160.
[18] 王震, 惠小健, 孙卫, 等. 周期参数扰动的T混沌系统周期轨道分析[J].数学杂志,2015, 35(3):672-682. WANG Zhen, HUI Xiaokang, SUN Wei, et al. Periodic orbits analysis of T chaotic system with periodic parametric perturbation[J]. Journal of Mathematic, 2015, 35(3):672-682.
[19] 雷腾飞, 王艳玲, 康杰, 等. 一类含有对数项T系统的混沌特性分析[J]. 贵州师范大学学报(自然版), 2018,36(1): 77-84. LEI Tengfei, WANG Yanling, KANG Jie, et al. Analysis on logarithmic T system and its chaos characteristics[J]. Journal of Guizhou Normal University(Naturnal Science), 2018, 36(1):77-84.
[20] POD Lubny. Fractional differential equations[M]. SanDiego, USA: Academic Press, 1999.
[21] 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.

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