多涡卷超混沌系统自适应滑模同步控制

doi:10.6040/j.issn.1672-3961.0.2014.155

摘要/Abstract

摘要： 研究了一类多涡卷超混沌系统的同步控制问题,同时考虑了不确定项和未知扰动的情况,提出了一种自适应滑模控制方案。综合利用滑模控制技术和自适应控制技术,消除了系统不确定性和未知扰动的影响,对于不确定性和未知扰动具有较好的鲁棒性。利用Lyapunov稳定性理论证明了系统同步误差渐近收敛到一个原点的小邻域内,系统渐近稳定。仿真结果验证了该方法的有效性。

关键词: 自适应控制, 多涡卷, 滑模控制, PI滑模面, 混沌同步, 超混沌

Abstract: An adaptive sliding mode control scheme was presented for the synchronization of a class of multiwing hyperchaotic system with uncertainties and unknown external disturbances. The sliding mode control and parameter adaptive principle were designed to realize the synchronization between the master system and slave system. Adaptive control technique and the sliding mode technique were both used to introduce robustness and eliminate systematic uncertainties and affections from external disturbances. It is proved that synchronization errors converge to a small neighbourhood of the origin by using Lyapunov stability theory. Finally, simulation results verified the effectiveness of the proposed control scheme.

Key words: multiwing, hyperchaos, sliding mode control, chaos sychronization, adaptive control, PI sliding mode

中图分类号:

TP273

孙美美, 胡云安, 韦建明. 多涡卷超混沌系统自适应滑模同步控制[J]. 山东大学学报(工学版), 2015, 45(6): 45-51.

SUN Meimei, HU Yun'an, WEI Jianming. Synchronization of multiwing hyperchaotic systems via adaptive sliding mode control[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2015, 45(6): 45-51.

参考文献

[1] PECORA L M, CAROLL T L. Synchronization in chaotic systems[J]. Physics Review Letters, 1990, 64(8):821-824.
[2] YASSEN M T. Controlling chaos and synchronization for new chaotic system using linear feedback control[J]. Chaos, Solitons & Fractals, 2005, 26(3):913-920.
[3] WANG F, LIU C. A new criterion for chaos and hyperchaos synchronization using linear feedback control[J]. Physics Letters(Section A), 2006, 360(2):274-278.
[4] RAFIKOV M, BALTHAZAR J M. On control and synchronization in chaotic and hyperchaotic systems via linear feedback control[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(7):1246-1255.
[5] CHEN H H, SHEU G J, LIN Y L, et al. Chaos synchronization between two different chaotic systems via nonlinear feedback control[J]. Nonlinear Analysis:Theory, Methods & Applications, 2009, 70(12):4393-4401.
[6] LV L, GUO Z A, ZHANG C. Synchronization between two different chaotic systems with nonlinear feedback control[J]. Chinese Physics, 2007, 16(6):1603-1607.
[7] CHEN M, CHEN W. Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems[J]. Chaos, Solitons & Fractals, 2009, 41(5):2716-2724.
[8] SALARIEH H, ALASTY A. Adaptive synchronization of two chaotic systems with stochastic unknown parameters[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(2):508-519.
[9] KEBRIAEI H, JAVAD YAZDANPANAH M. Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(2):430-441.
[10] LI X F, LEUNG A C S, LIU X J, et al. Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters[J]. Nonlinear Analysis:Real World Applications, 2010, 11(4):2215-2223.
[11] KOOFIGAR H R, HOSSEINNIA S, SHEIKHOLESLAM F. Robust adaptive synchronization of uncertain unified chaotic systems[J]. Nonlinear Dynamics, 2010, 59(3):477-483.
[12] WU X J, LU H T. Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters[J]. Chaos, Solitons & Fractals, 2011, 44(10):802-810.
[13] YANG C C. Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller[J]. Nonlinear Dynamics, 2011, 63(3):447-454.
[14] LIU P, LIU S. Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances[J]. Nonlinear Dynamics, 2012, 70(1):585-599.
[15] WANG C, GE S S. Adaptive synchronization of uncertain chaotic systems via backstepping design[J]. Chaos, Solitons & Fractals, 2001, 12(7):1199-1206.
[16] FARIVAR F, SHOOREHDELI M A, NEKOUI M A, et al. Generalized projective synchronization for chaotic systems via Gaussian radial basis adaptive backstepping control[J]. Chaos, Solitons & Fractals, 2009, 42(2):826-839.
[17] NJAH A N. Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques[J]. Nonlinear Dynamics, 2010, 61(1-2):1-9.
[18] YU B Y, LI H X. Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design[J]. Nonlinear Analysis:Real World Applications, 2011, 12(1):388-393.
[19] LI H Y, HU Y A. Backstepping-based synchronization control of cross-strict feedback hyper-chaotic systems[J]. Chinese Physics Letters, 2011, 28(12):120508.
[20] JI D H, JEONG S C, PARK J H, et al. Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer[J]. Nonlinear Dynamics, 2012, 69(3):1125-1136.
[21] LI S Y, YANG C H, LIN C T, et al. Adaptive synchronization of chaotic systems with unknown parameters via new backstepping strategy[J]. Nonlinear Dynamics, 2012, 70(3):2129-2143.
[22] LI H Y, HU Y A. Robust sliding-mode backstepping design for synchronization control of cross-strict feedback hyperchaotic systems with unmatched uncertainties[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(10):3904-3913.
[23] POURMAHMOOD M, KHANMOHAMMADI S, ALIZADEH G. Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(7):2853-2868.
[24] YANG L, YANG J. Robust finite-time convergence of chaotic systems via adaptive terminal sliding mode scheme[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(6):2405-2413.
[25] AGHABABA M P, HEYDARI A. Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities[J]. Applied Mathematical Modelling, 2012, 36(4):1639-1652.
[26] AGHABABA M P, AKBARI M E. A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances[J]. Applied Mathematics and Computation, 2012, 218(9):5757-5768.
[27] 王银河,高子林,王钦若,等.基于自适应模糊逻辑系统的一类混沌系统同步控制[J]. 控制与决策, 2013, 28(9):1309-1314. WANG Y H, GAO Z L, WANG Q R, et al. Synchronization control for a class of chaotic systems based on adaptive fuzzy logic systems[J]. Control and Decision, 2013, 28(9):1309-1314.
[28] LI S Y, YANG C H, CHEN S A, et al. Fuzzy adaptive synchronization of time-reversed chaotic systems via a new adaptive control strategy[J]. Information Sciences, 2013, 222:486-500.
[29] XU J X, YAN R. Synchronization of chaotic systems via learning control[J]. International journal of bifurcation and Chaos, 2005, 15(12):4035-4041.
[30] SUN Y P, LI J M, WANG J A, et al. Generalized projective synchronization of chaotic systems via adaptive learning control[J]. Chinese Physics B, 2010, 19(2):020505.
[31] SUYKENS J A K, VANDEWALLE J. Generation of n-double scrolls(n=1, 2, 3, 4,…)[J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications, 1993, 40(11):861-867.
[32] ZHONG G Q, MAN K F, CHEN G. A systematic approach to generating n-scroll attractors[J]. International Journal of Bifurcation and Chaos, 2002, 12(12):2907-2915.
[33] WANG F Q, LIU C X. Generation of multi-scroll chaotic attractors via the saw-tooth function[J]. International Journal of Modern Physics B, 2008, 22(15):2399-2405.
[34] FEI Y, CHUN-HUA W, JIN-WEN Y, et al. Novel four-dimensional autonomous chaotic system generating one-, two-, three-and four-wing attractors[J]. Chinese Physics B, 2011, 20(11):110505.
[35] 吴忠强,邝钰. 多涡卷混沌系统的广义同步控制[J]. 物理学报,2009,58(10):6823-6827. WU Z Q, KUANG Y. Generalized synchronization control of multi-scroll chaotic systems[J]. Acta Physica Sinica, 2009, 58(10):6823-6827.
[36]余飞,王春华,胡燕,等. 具有完全不确定参数的五项双曲型混沌系统的投影同步[J]. 物理学报,2012,61(6):060505.YU Fei, WANG Chunhua, HU Yan, et al. Projective synchronization of a five-term hyperbolic-type chaotic system with fully uncertain parameters[J]. Acta Physica Sinica, 2012, 61(6):060505.
[37]刘恒,余海军,向伟. 带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):180503.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):180503.
[38]ELABBASY E M, AGIZA H N, EL-DESSOKY M M. Adaptive synchronization for four-scroll attractor with fully unknown parameters[J]. Physics Letters A, 2006, 349(1):187-191.
[39] SUNDARAPANDIAN V. Global chaos synchronization of four-scroll and four-wing attractors by active nonlinear control[J]. International Journal on Computer Science and Engineering, 2011, 3(5):2145-2155.
[40] YU Simin, LU Jinhu. Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops[J]. IEEE Transactions on Circuits and Systems, 2012, 59(5):1015-1027.

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