混沌系统的几种同步控制方法及其应用研究
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摘要
混沌作为一种复杂的非线性运动行为,在生物学、物理学、化学、工程学和信息学等领域得到了广泛的研究。由于它的初值极端敏感性、高度随机性以及非线性方程的确定性,一直受到研究者的极大关注。自九十年代以来,混沌同步控制的研究发展迅速,并取得了很多成果。
本文基于非线性系统控制理论,研究了整数阶混沌系统和分数阶混沌系统的同步控制方法及其应用。论文的主要研究成果如下:
(1)提出了一种新的复合快速混沌同步控制方法
综合驱动-响应同步和耦合同步控制方法的优点,提出了一种新的复合快速同步控制方法。Lorenz混沌系统和Liu混沌系统的仿真实验结果表明,该方法大大缩短了混沌系统的同步时间,改善了同步的动态性能。
(2)提出了一个新的MLS混沌系统的单变量驱动同步和状态观测器同步两种方法
在深入分析新的四维分段MLS混沌系统混沌特性的基础上,首先提出了单变量驱动同步法,该方法结构简单,易于实现;然后提出了MLS混沌系统的状态观测器同步方法,该方法同步控制器形式多样,为工程应用提供了多种构造方案。
(3)提出了异结构混沌系统的Q-S同步和广义投影同步两种方法
首先,提出了超混沌Liu混沌系统和Genesio混沌系统的Backstepping同步方法,设计了单一驱动和多驱动两种同步控制器,实现了Q-S同步形式,简化了控制器的结构。然后,提出了超混沌Wang系统和超混沌Liu系统的改进广义投影同步方法,该方法应用灵活,同步控制器具有多个可变参数,能够调节混沌系统的同步速度和同步形式。
(4)提出了一个新的分数阶LS混沌系统的完全同步和广义投影同步两种方法
在深入分析新的分数阶LS混沌系统动力学特性的基础上,首先基于Laplace变换理论提出了该分数阶系统的完全同步控制方法,控制器结构简单,同步效果好;接着应用线性分数阶系统的稳定性理论,提出分数阶LS混沌系统的广义投影同步控制方法,控制器的设计利用原驱动系统的信息较少,易于实现。
(5)研究了混沌在保密通信中的应用
首先基于区间同步-恢复记忆实现混沌保密通信的思想,成功地实现了信号的完整提取;然后研究了基于状态观测器的超混沌保密通信方案,增强了保密性,同时也有利于实际应用。最后提出利用双向耦合映象格子系统产生混沌序列的方法,并将改进的时空混沌序列成功应用于数字图像加密方法中。
Chaotic systems are well known for their very complex nonlinear systems, and have been intensively studied in various fields such as biology, physics, chemistry, engineering and information. Since it has the characteristics of sensitivity to initial values, high randomicity and certainty to nonlinear equations, chaos attracts great attentions from investigators. Chaotic synchronization is an important research aspect in chaotic science. Since 1990, chaos synchronization has achieved rapid development, and there have lots of remarkable results reported about it.
Based on control theories of nonlinear systems, this dissertation studies the synchronization control methods and applications of integral-order and fractional-order chaotic systems. The main contributions are listed as follows:
(1) A new complex fast synchronization control method is proposed for chaotic systems.
Synthesizing the advantages of drive-response synchronization and coupled synchronization methods, a new complex fast synchronization control method is proposed. The simulation researches of Lorenz chaotic system and Liu chaotic system show that this method obviously shortens the synchronization time of chaotic systems and improves the synchronization dynamic performance.
(2) Single-driving synchroniaiton and state observation synchronition methods are proposed for a new MLS chaotic system.
Firstly, based on the analysis of the chaotic characteristic for a new four-dimensional piecewise MLS chaotic system, a single-driving synchronization method is proposed. This method has simple structures and is esay to be realized. Secondly, the state observation synchronization method is proposed. This method owns various formats in controllers, which provides multiforms schemes for project applications.
(3) Q-S synchronization and generalized projective synchronization methods are proposed for different structure chaotic systems.
Firstly, the Backstepping synchronization method is proposed for hyperchaotic Liu chaotic system and Genesio chaotic system. In this method single-driving and multi-driving synchronization controllers are designed to realize Q-S synchronization format, which simplifies the structures of controllers. Secondly, the improved generalized projective synchronization method is proposed for hyperchaotic Wang system and hyperchaotic Liu system. This method is agile to change the mutative parameters in synchronization controllers, which can adjust the synchronization speed and formats for chaotic systems.
(4) The complete synchronization and generalized projective synchronization methods are proposed for a new fractional-order LS chaotic system.
Firstly, after analyzing the dynamical characteristic for a new fractional-order LS chaotic system, the complete synchronization control method is proposed for this fractional-order system based on Laplace transform theory. The structures of controllers are simple and the effect of synchronization is satisfied. Secondly, the generalized projective synchronization control method is proposed for fractional-order LS system applying the stability theory of linear fractional-order system. The designs of controllers use less information of original drive system, so it is easy to be realized.
(5) The chaotic applications are studied in secure communication.
Firstly, the realization of chaotic secure communication based on the method of interval synchronization-recalling memory is provided, and the signal can be recovered wholly and exactly. Secondly, the scheme of hyperchaotic secure communication is studied based on state observation. The method enhances the security and is prone to realize in fact with broad applicability. Thirdly, spatiotemporal chaotic sequences are achieved using the two-way coupled map lattice system. And then the improved spatiotemporal chaotic sequences are successfully applied in encrypt method of digital image.
本文基于非线性系统控制理论,研究了整数阶混沌系统和分数阶混沌系统的同步控制方法及其应用。论文的主要研究成果如下:
(1)提出了一种新的复合快速混沌同步控制方法
综合驱动-响应同步和耦合同步控制方法的优点,提出了一种新的复合快速同步控制方法。Lorenz混沌系统和Liu混沌系统的仿真实验结果表明,该方法大大缩短了混沌系统的同步时间,改善了同步的动态性能。
(2)提出了一个新的MLS混沌系统的单变量驱动同步和状态观测器同步两种方法
在深入分析新的四维分段MLS混沌系统混沌特性的基础上,首先提出了单变量驱动同步法,该方法结构简单,易于实现;然后提出了MLS混沌系统的状态观测器同步方法,该方法同步控制器形式多样,为工程应用提供了多种构造方案。
(3)提出了异结构混沌系统的Q-S同步和广义投影同步两种方法
首先,提出了超混沌Liu混沌系统和Genesio混沌系统的Backstepping同步方法,设计了单一驱动和多驱动两种同步控制器,实现了Q-S同步形式,简化了控制器的结构。然后,提出了超混沌Wang系统和超混沌Liu系统的改进广义投影同步方法,该方法应用灵活,同步控制器具有多个可变参数,能够调节混沌系统的同步速度和同步形式。
(4)提出了一个新的分数阶LS混沌系统的完全同步和广义投影同步两种方法
在深入分析新的分数阶LS混沌系统动力学特性的基础上,首先基于Laplace变换理论提出了该分数阶系统的完全同步控制方法,控制器结构简单,同步效果好;接着应用线性分数阶系统的稳定性理论,提出分数阶LS混沌系统的广义投影同步控制方法,控制器的设计利用原驱动系统的信息较少,易于实现。
(5)研究了混沌在保密通信中的应用
首先基于区间同步-恢复记忆实现混沌保密通信的思想,成功地实现了信号的完整提取;然后研究了基于状态观测器的超混沌保密通信方案,增强了保密性,同时也有利于实际应用。最后提出利用双向耦合映象格子系统产生混沌序列的方法,并将改进的时空混沌序列成功应用于数字图像加密方法中。
Chaotic systems are well known for their very complex nonlinear systems, and have been intensively studied in various fields such as biology, physics, chemistry, engineering and information. Since it has the characteristics of sensitivity to initial values, high randomicity and certainty to nonlinear equations, chaos attracts great attentions from investigators. Chaotic synchronization is an important research aspect in chaotic science. Since 1990, chaos synchronization has achieved rapid development, and there have lots of remarkable results reported about it.
Based on control theories of nonlinear systems, this dissertation studies the synchronization control methods and applications of integral-order and fractional-order chaotic systems. The main contributions are listed as follows:
(1) A new complex fast synchronization control method is proposed for chaotic systems.
Synthesizing the advantages of drive-response synchronization and coupled synchronization methods, a new complex fast synchronization control method is proposed. The simulation researches of Lorenz chaotic system and Liu chaotic system show that this method obviously shortens the synchronization time of chaotic systems and improves the synchronization dynamic performance.
(2) Single-driving synchroniaiton and state observation synchronition methods are proposed for a new MLS chaotic system.
Firstly, based on the analysis of the chaotic characteristic for a new four-dimensional piecewise MLS chaotic system, a single-driving synchronization method is proposed. This method has simple structures and is esay to be realized. Secondly, the state observation synchronization method is proposed. This method owns various formats in controllers, which provides multiforms schemes for project applications.
(3) Q-S synchronization and generalized projective synchronization methods are proposed for different structure chaotic systems.
Firstly, the Backstepping synchronization method is proposed for hyperchaotic Liu chaotic system and Genesio chaotic system. In this method single-driving and multi-driving synchronization controllers are designed to realize Q-S synchronization format, which simplifies the structures of controllers. Secondly, the improved generalized projective synchronization method is proposed for hyperchaotic Wang system and hyperchaotic Liu system. This method is agile to change the mutative parameters in synchronization controllers, which can adjust the synchronization speed and formats for chaotic systems.
(4) The complete synchronization and generalized projective synchronization methods are proposed for a new fractional-order LS chaotic system.
Firstly, after analyzing the dynamical characteristic for a new fractional-order LS chaotic system, the complete synchronization control method is proposed for this fractional-order system based on Laplace transform theory. The structures of controllers are simple and the effect of synchronization is satisfied. Secondly, the generalized projective synchronization control method is proposed for fractional-order LS system applying the stability theory of linear fractional-order system. The designs of controllers use less information of original drive system, so it is easy to be realized.
(5) The chaotic applications are studied in secure communication.
Firstly, the realization of chaotic secure communication based on the method of interval synchronization-recalling memory is provided, and the signal can be recovered wholly and exactly. Secondly, the scheme of hyperchaotic secure communication is studied based on state observation. The method enhances the security and is prone to realize in fact with broad applicability. Thirdly, spatiotemporal chaotic sequences are achieved using the two-way coupled map lattice system. And then the improved spatiotemporal chaotic sequences are successfully applied in encrypt method of digital image.
引文
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