Sliding mode adaptive synchronization for a class of fractional-order chaotic systems with uncertainties
-
摘要: 基于滑模自适应控制理论、Lyapunov稳定性理论和分数阶线性系统稳定性理论,在考虑系统存在模型不确定和外部扰动的情况下,选用一种具有较强鲁棒性的分数阶滑模曲面,设计了合适的自适应滑模控制器。所设计的控制器能够将系统状态控制到滑模面上,实现两个不确定分数阶混沌系统的同步,且不需事先知道不确定项上界。该控制器结构简单,控制代价小,具有较好的通用性,对未知扰动具有较强的鲁棒性。数值仿真验证了该方法的正确性和有效性。Abstract: A fractional-order sliding mode adaptive control approach was introduced to synchronize chaos of a class of fractional-order chaotic systems with uncertainties. The effects of model uncertainties and external disturbances were fully taken into account. An appropriate robust fractional sliding mode adaptive controller was designed by adopting a fractional sliding surface with strong robustness, and using sliding mode adaptive control theory, Lyapunov stability theory and fractional-order linear systems stability theory. The control law can ensure the occurrence of the sliding motion, and achieve synchronization between the drive system and response system. The upper bound of uncertainties was not needed in the proposed controller. The designed controller is not complicated mathematically and easy to implement. The fractional adaptive sliding mode control approach can be applied to control a broad range of nonlinear fractional-order chaotic systems with uncertainties. Numerical simulation was presented to show the efficiency and applicability of the proposed control strategy.
-
[1] 石晓荣,张明廉.一种基于混沌神经网络的拟人智能控制方法[J].北京航空航天大学学报,2004,30(9):889-892 Shi Xiaorong,Zhang Minglian.Human-imitating control based on chaotic neural networks[J].Journal of Beijing University of Aeronautics And Astronautics,2004,30(9):889-892(in Chinese) [2] 张俊锋,沈云琴,张晓丽.利用滑模控制实现不确定混沌系统投影同步[J].计算机测量与控制,2011,19(8):1912-1914 Zhang Junfeng,Sheng Yunqin,Zhang Xiaoli.Projective synchro-nization of chaotic system with uncertainties based on sliding mode control[J].Computer Measurement & Control,2011,19(8):1912-1914(in Chinese) [3] Kinzel W,Englert A,Kanter I.On chaos synchronization and secure communication[J].Philosophical Transactions of the Royal Society A:Mathematical,Physical and Engineering Sciences,2010,368(1911):379-389 [4] 李东,邓良明,杜永霞,等.分数阶超混沌Chen系统和分数阶超混沌Rossler系统的异结构同步[J].物理学报,2012,61(5):050502-1-9 Li Dong,Deng Liangming,Du Yongxia,et al.Synchronization for fractional order hyperchaotic Chen system and fractional order hyperchaotic Rossler system with different structure[J].Acta Physica Sinica,2012,61(5):050502-1-9(in Chinese) [5] 谭文,张敏,李志攀.分数阶互联电力系统混沌震荡及其同步控制[J].湖南科技大学学报,2011,26(2):74-77 Tan Wen,Zhang Min,Li Zhipan.Chaotic oscillation of interconn-ecred power system and its synchronization[J].Hunan Univers-ity of Science & Technology,2011,26(2):74-77(in Chinese) [6] 胡建彬,韩焱,赵灵冬.分数阶系统的一种稳定性判定定理及在分数阶统一混沌系统同步中的应用[J].物理学报,2009,58(7):4002-4007 Hu Jianbin,Han Yan,Zhao Lingdong.A stability theorem about fractional systems and synchronizing fractional unified chaotic systems based on the theorem[J].Acta Physica Sinica,2009,58(7):4002-4007(in Chinese) [7] 孙光辉.分数阶混沌系统的控制及同步研究[D].哈尔滨:哈尔滨工业大学,2010 Sun Guanghui.The research on the fractional chaos synchronizat-ion and control[D].Harbin:Harbin Institute of Technology,2010(in Chinese) [8] 马铁东,江伟波,浮洁,等.一类分数阶混沌系统的自适应同步[J].物理学报,2012,61(16):160506-1-6 Ma Tiedong,Jiang Weibo,Fu Jie,et al.Adaptive synchronization of a class of fractional-order chaotic systems[J].Acta Physica Sinica,2012,61(16):160506-1-6(in Chinese) [9] Zaid O.A note on phase synchronization in coupled chaotic fractional order systems[J].Nonlinear Analysis:Real World Applications,2012,13(2):779-789 [10] 黄丽莲,齐雪.基于自适应滑模控制的不同维分数阶混沌系统的同步[J].物理学报,2013,62(8):080507-1-7 Huang Lilian,Qi Xue.The synchronization of fractional order chaotic systems with different orders based on adaptive sliding mode control[J].Acta Physica Sinica,2013,62(8):080507-1-7(in Chinese) [11] Arman K B,Fallahi K,Pariz N,et al.A chaotic secure communi-cation scheme using fractional chaotic systems based on an exte-nded fractional Kalman filter[J].Communications in Nonlinear Science and Numerical Sumulation,2009,14(3):863-879 [12] 邓玮,方洁,吴振军,等.含有不确定项的混沌系统自适应修正函数投影同步[J].物理学报,2012,61(14):140503-1-7 Deng Wei,Fang Jie,Wu Zhenjun,et al.Adaptive modified function projective synchronizatio of a class of chaotic systems with uncertainties[J].Acta Physica Sinica,2012,61(14):140503-1-7(in Chinese) [13] Hifer R.Applications of fractional calcus in physics [M].New Jersey:World Scientific,2001:44-47 [14] Matignon D.Stability results for fractional differential equations with application control processing[J].IMACS,IEEE-SMC,1996,17(6):963-968 [15] Wang J M,Xiong X H,Zhang Y B.Extending synchronization scheme to fractional-order Chen systems[J].Physica A:Statistical Mechanics and its Applications,2006,370(2):279-285
点击查看大图
计量
- 文章访问数: 961
- HTML全文浏览量: 53
- PDF下载量: 482
- 被引次数: 0