参数未知多响应混沌系统的同步及参数估计
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摘要
研究了一种单驱动多响应的不确定异构混沌系统的同步及参数估计问题。利用Lorenz系统同时驱动Yang系统和Liu系统(三个系统的参数均未知),构成一个单驱动多响应的不确定异构混沌系统。基于Lyapunov稳定性定理和自适应控制方法,给出自适应控制器的表达式和参数自适应率;引入尺度因子,研究了该单驱动多响应混沌系统两种不同形式的混合同步,并对未知参数进行估计,理论证明了该方法的可行性。仿真结果表明单驱动多响应的不确定异构混沌系统可以实现较好的同步,能准确地估计出系统中所有未知参数的值。
The synchronization and parameter estimation of an uncertain heterogeneous chaotic system with single-drive and multiple-response are investigated.By using Lorenz system to drive Yang system and Liu system simultaneously(parameters of the three systems are unknown),an uncertain heterogeneous chaotic system with single-drive and multiple-response is constructed.Based on Lyapunov stability theory and adaptive control method,the expression of adaptive controller and updating rule of parameters are given.Two different forms of mixed synchronization of the chaotic system with single-drive and multiple-response are investigated by,introducing the scaling factor,and the unknown parameters are estimated.The feasibity of the method is proved theoretically.The simulation results show that the uncertain heterogeneous chaotic system with single-drive and multiple-response can achieve better synchronization and accurately estimate the values of all unknown parameters in the system.
The synchronization and parameter estimation of an uncertain heterogeneous chaotic system with single-drive and multiple-response are investigated.By using Lorenz system to drive Yang system and Liu system simultaneously(parameters of the three systems are unknown),an uncertain heterogeneous chaotic system with single-drive and multiple-response is constructed.Based on Lyapunov stability theory and adaptive control method,the expression of adaptive controller and updating rule of parameters are given.Two different forms of mixed synchronization of the chaotic system with single-drive and multiple-response are investigated by,introducing the scaling factor,and the unknown parameters are estimated.The feasibity of the method is proved theoretically.The simulation results show that the uncertain heterogeneous chaotic system with single-drive and multiple-response can achieve better synchronization and accurately estimate the values of all unknown parameters in the system.
引文
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[2]Li Guoliang,Wu Xiang.Adaptive synchronization of chaotic neural networks with mixed time delays and unknown parameters[J].ICIC Express Letters,2015,9(3):883-890.
[3]Handa H,Sharma B B.Synchronization of a set of coupled chaotic Fitz-Hugh-Nagumo and Hindmarsh-Rose neurons with external electrical stimulation[J].Nonlinear Dynamics,2016,85(3):1517-1532.
[4]Lu Renkuan,Shi Peng,Su Hongye,et al. Synchronization of general chaotic neural networks with nonuniform sampling and packet missing:A switched system approach[J].IEEE Transactions on Neural Networks and Learning Systems,2018,29(3):523-533.
[5]Cai Guoliang,Yao Lan,Hu Pei,et al. Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters[J].Discrete and Continuous Dynamical Systems Series B,2013,18(8):2019-2028.
[6]Zhou Changqin,Shi Limin.Chaos synchronization of a class of integral-order and fractional-order financial systems[J].Journal of Xinxiang University(新乡学院学报),2016,33(9):14-16(in Chinese).
[7]Fang Xiaodan,Cai Guoliang.A single-input linear controller for complete synchronization of a delay financial hyperchaotic system[J].Journal of Information and Computing Science,2014,9(3):224-232.
[8]Monifi F,Zhang Jing,Ozdemir S K,et al.Optomechanically induced stochastic resonance and chaos transfer between optical fields[J].Nature Photonics,2016,10(6):399-405.
[9]Nazhan S,Ghassemlooy Z.Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback[J].Chaos,2016,26(1):013109.
[10]Cicek S,Ferikoglu A.A new 3D chaotic system:Dynamical analysis,electronic circuit design,active control synchronization and chaotic masking communication application[J].Optik-International Journal for Light and Electron Optics,2016,127(8):4024-4030.
[11]Garzagonzalez E,Posadascastillo C.Chaotic synchronization of irregular complex network with hysteretic circuitlike oscillators in Hamiltonian form and its application in private communications[J].Revista Mexicana De Fisica,2016,.62(1):51-59.
[12]Hassan M F.Synchronization of uncertain constrained hyperchaotic systems and chaos-based secure communications via a novel decomposed nonlinear stochastic estimator[J].Nonlinear Dynamics,2016,83(4):2183-2211.
[13]Vaseghi B,Pourmina M A.Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control[J].Nonlinear Dynamics,2017,89(3):1689-1704.
[14]Abd M H,Tahir F R.An adaptive observer synchronization using chaotic time-delay system for secure communication[J].Nonlinear Dynamics,2017,90(4):2583-2598.
[15]Saha C,Hossain M F.Improving the security of spatial domain based digital image watermarking using chaotic map and cellular automationg[J].International Journal of Image Graphics and Signal Processing,2016,8(1):51-58.
[16]Noui O,Beloucif A.Secure image encryption scheme based on polar decomposition and chaotic map[J].International Journal of Information and Communication Technology,2016,10(4):437-453.
[17]Li Guozheng,Zhang Bo.A novel weak signal detection method via chaotic synchronization using Chua's circuit[J].IEEE Transactions on Industrial Electronics,2017,64(3):2255-2265.
[18]Jiang Cuimei,Zhang Fangfang,Li Tongxing.Synchronization and antisynchronization of N-coupled fractionalorder complex chaotic systems with ring connection[J].Mathematical Methods in the Applied Sciences,2018,41(7):2625-2638.
[19]Othman A A,Noorani M S M.Adaptive dual synchronization of chaotic and hyperchaotic systems with fully uncertain parameters[J].Optik-International Journal for Light and Electron Optics,2016,127(19):7852-7864.
[20]Othman A A,Noorani M S M.Adaptive dual anti-synchronization of chaotic systems with fully uncertain parameters[J].Optik-International Journal for Light and Electron Optics,2016,127(22):10478-10489.
[21]Ouannas A,Azar A T.A new type of hybrid synchronization between arbitrary hyperchaoticmaps[J].International Journal of Machine Learning and Cybernetics,2017,8(6):1887-1894.
[22]Vargas J A R,Grzeidak E.An adaptive scheme for chaotic synchronization in the presence of uncertain parameter and disturbances[J].Neurocomputing,2016,174(5):1038-1048.
[23]Luo Ruizi,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.
[24]Behinfaraz R,Badamchizadeh M.An adaptive method to parameter identification and synchronization of fractional-order chaotic systems with parameter uncertainty[J].Applied Mathematical Modelling, 2016,40(7-8):4468-4479.
[25]Li Xianli,Dou Xueying,Zhao Liyang.Research on the chaotic synchronization for the fractional-order colpitts system with uncertain parameters[J].Process Automation Instrumentation,2017,38(3):22-29.
[26]Jia Feilei,Xu Wei.Generalized synchronization of different orders of chaotic systems with unknown parameters and parameter identification[J].Acta Physica Sinica(物理学报)2007,56(10):5640-5647(in Chinese).
[27]Zhang Youan,Yu Mingzhe,Wu Huali.Multi-drive-one response synchronization of fractional-order chaotic systems with uncertainties[J].Chinese Journal of Electronics,2016,44(3):607-612.
[28]Zhu Huijian,Zeng Caibin.Scaling and mixed synchronization for different chaotic systems with,totally unknown parameters[J].Control Theory and Application(控制理论与应用),2015,32(3):341-346(in Chinese).
[29]Huang Wendi,Min Fuhong.Complete synchronization of single-drive and multiple-response fractional-order chaotic systems[J].Journal of Nanjing Normal University(Engineering and Technology Edition)(南京师范大学学报(工程技术版)),2015,15(2):1-8(in Chinese).