毕业论文 混沌系统控制与同步若干问题的研究.doc
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毕业论文 混沌系统控制与同步若干问题的研究,摘要混沌运动是自然界中客观存在的、最终有界的、有一定随机规则的、非常复杂的运动形式。近十几年来，混沌科学与其它科学互相渗透，在工程领域、智能信息处理、计算科学、通讯领域、生命科学和社会经济等领域有着广泛的应用前景，混沌控制与混沌同步控制成为了非线性科学中的研究热点。但混沌控制及混沌同步理论尚不完善，许多混沌控制及同步方...
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摘 要
混沌运动是自然界中客观存在的、最终有界的、有一定随机规则的、非常复杂的运动形式。近十几年来，混沌科学与其它科学互相渗透，在工程领域、智能信息处理、计算科学、通讯领域、生命科学和社会经济等领域有着广泛的应用前景，混沌控制与混沌同步控制成为了非线性科学中的研究热点。但混沌控制及混沌同步理论尚不完善，许多混沌控制及同步方法有待进一步发掘，如何设计简单实用的控制器需要进一步研究。本文针对混沌系统控制（包括同步控制）的一些问题进行研究，主要包括以下几个方面：
1. 由于受系统物理器件的限制，混沌系统的线性输入不可避免的存在干扰，从而引起线性输入变成非线性输入。运用滑模控制方法，严格证明了混沌系统在非线性输入和两种情况的外部干扰（即匹配扰动和非匹配扰动）下实现稳定控制，改进和推广了一些现有文献中仅限于无扰动或匹配扰动，得到了更系统的结论。
2. 根据二阶滑模的概念和Lyapunov函数稳定性理论，针对一类带有非匹配外部扰动的混沌系统，提出了非奇异二阶滑模控制方法，不仅使得混沌的状态向量趋近到平衡点附近的邻域，而且抖动现象得到消除。数值仿真验证其优于现有一些文献的方法。
3. 通过引入一个非线性状态反馈控制器到一类三维混沌系统，产生一新的四维系统，运用Lyapunov指数对该系统进行分岔分析，验证其结构具有超混沌行为，再运用反馈控制方法和脉冲控制方法对其进行稳定性控制。
4. 讨论混沌系统的修正投影同步问题，分两种情况，一是混沌系统出现参数不确定项，外部扰动和带有死区非线性输入的修正投影同步；二是混沌系统的外部扰动产生于未知外源系统的修正投影同步，并给出了相应的数值仿真，证实了所提出控制策略的有效性。
5. 讨论一类含有传递信号混沌系统的估计问题，基于观测器方法和自适应 同步相关概念，视混沌系统的传递信号为系统外在的状态变量，以可测的输出向量构建状态观测器，通过设置合适的条件，减小外在扰动和未知参数的影响，使得观测器的估计误差状态实现自适应 同步，从而估计传递信号的相关信息。
6. 对全文工作进行了总结，并对以后进一步的工作进行了展望。
关键词：混沌系统， Lyapunov函数，滑模面，稳定性，同步，观测器 ，滑模控制
ABSTRACT
Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to engineering, intelligent information processing, computational science, communications, life sciences, socio-economic areas and so on. The control and synchr- onization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be further investigation, for example, to design simple and effective controllers. In this thesis, some problems in control and parameter identification of chaos systems are studied. The main work and research results are as follows:
1. Due to the limitations of physical devices, there exists the inevitable interference in linear input so that causes the linear input into the nonlinear input. Using sliding mode control, The proof of the chaotic systems to be realized stable under the effection of two different dirturbance (ie, matched the external dirtuebance and unmatched external dirturbance) is strictly proved. It improves and extends the results in existing literature that only to discuss the case that no disturbance or matching external disturbance and get more general conclusions.
2. According to the concept of second-order sliding mode and the stability theory of Lyapunov function, the stabilization for a class of chaotic systems with unmatiched external disturbances is investigated. Using non-sigular second-order sliding mode control approach, makes the state of chaotic system converge to the neighborhood of the equilibrium point and the chattering phenomenon has been eliminated. Numerical simulations show its better than the existing method of some literatures.
3. By introducing a nonlinear state feedback controller into a three-dimensional chaotic system to produce a new 4D system. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. This can verify the system has hyperchaotic behavior. Feedback control and implusive control approaches are employed here to stabilize the new hyperchaotic system.
4. Discuss the modified projective synchronization of chaotic systems under two conditions, one is that the chaotic systems suffers parameter uncertainty, external disturbance and dead-zone nonlinear input; the orther is that the disturbances of chaotic systems generate the unknown exogenous systems. The corresponding numerical simulation show the effectiveness of proposed methods.
5. Discuss a class of chaotic systems with transimitted signal. Based on the concepts of observer and adaptive synchronization, taking the transimitted signal as an external system state and designing an observer by using the measured output to estimate the state and transimitted signal. By setting the suitable conditions to reduce the influence of the external disturbance and unknown parameters so that estimation error of the observer can achieve adaptive synchronization. Then, the transmitted signal can be..
混沌运动是自然界中客观存在的、最终有界的、有一定随机规则的、非常复杂的运动形式。近十几年来，混沌科学与其它科学互相渗透，在工程领域、智能信息处理、计算科学、通讯领域、生命科学和社会经济等领域有着广泛的应用前景，混沌控制与混沌同步控制成为了非线性科学中的研究热点。但混沌控制及混沌同步理论尚不完善，许多混沌控制及同步方法有待进一步发掘，如何设计简单实用的控制器需要进一步研究。本文针对混沌系统控制（包括同步控制）的一些问题进行研究，主要包括以下几个方面：
1. 由于受系统物理器件的限制，混沌系统的线性输入不可避免的存在干扰，从而引起线性输入变成非线性输入。运用滑模控制方法，严格证明了混沌系统在非线性输入和两种情况的外部干扰（即匹配扰动和非匹配扰动）下实现稳定控制，改进和推广了一些现有文献中仅限于无扰动或匹配扰动，得到了更系统的结论。
2. 根据二阶滑模的概念和Lyapunov函数稳定性理论，针对一类带有非匹配外部扰动的混沌系统，提出了非奇异二阶滑模控制方法，不仅使得混沌的状态向量趋近到平衡点附近的邻域，而且抖动现象得到消除。数值仿真验证其优于现有一些文献的方法。
3. 通过引入一个非线性状态反馈控制器到一类三维混沌系统，产生一新的四维系统，运用Lyapunov指数对该系统进行分岔分析，验证其结构具有超混沌行为，再运用反馈控制方法和脉冲控制方法对其进行稳定性控制。
4. 讨论混沌系统的修正投影同步问题，分两种情况，一是混沌系统出现参数不确定项，外部扰动和带有死区非线性输入的修正投影同步；二是混沌系统的外部扰动产生于未知外源系统的修正投影同步，并给出了相应的数值仿真，证实了所提出控制策略的有效性。
5. 讨论一类含有传递信号混沌系统的估计问题，基于观测器方法和自适应 同步相关概念，视混沌系统的传递信号为系统外在的状态变量，以可测的输出向量构建状态观测器，通过设置合适的条件，减小外在扰动和未知参数的影响，使得观测器的估计误差状态实现自适应 同步，从而估计传递信号的相关信息。
6. 对全文工作进行了总结，并对以后进一步的工作进行了展望。
关键词：混沌系统， Lyapunov函数，滑模面，稳定性，同步，观测器 ，滑模控制
ABSTRACT
Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to engineering, intelligent information processing, computational science, communications, life sciences, socio-economic areas and so on. The control and synchr- onization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be further investigation, for example, to design simple and effective controllers. In this thesis, some problems in control and parameter identification of chaos systems are studied. The main work and research results are as follows:
1. Due to the limitations of physical devices, there exists the inevitable interference in linear input so that causes the linear input into the nonlinear input. Using sliding mode control, The proof of the chaotic systems to be realized stable under the effection of two different dirturbance (ie, matched the external dirtuebance and unmatched external dirturbance) is strictly proved. It improves and extends the results in existing literature that only to discuss the case that no disturbance or matching external disturbance and get more general conclusions.
2. According to the concept of second-order sliding mode and the stability theory of Lyapunov function, the stabilization for a class of chaotic systems with unmatiched external disturbances is investigated. Using non-sigular second-order sliding mode control approach, makes the state of chaotic system converge to the neighborhood of the equilibrium point and the chattering phenomenon has been eliminated. Numerical simulations show its better than the existing method of some literatures.
3. By introducing a nonlinear state feedback controller into a three-dimensional chaotic system to produce a new 4D system. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. This can verify the system has hyperchaotic behavior. Feedback control and implusive control approaches are employed here to stabilize the new hyperchaotic system.
4. Discuss the modified projective synchronization of chaotic systems under two conditions, one is that the chaotic systems suffers parameter uncertainty, external disturbance and dead-zone nonlinear input; the orther is that the disturbances of chaotic systems generate the unknown exogenous systems. The corresponding numerical simulation show the effectiveness of proposed methods.
5. Discuss a class of chaotic systems with transimitted signal. Based on the concepts of observer and adaptive synchronization, taking the transimitted signal as an external system state and designing an observer by using the measured output to estimate the state and transimitted signal. By setting the suitable conditions to reduce the influence of the external disturbance and unknown parameters so that estimation error of the observer can achieve adaptive synchronization. Then, the transmitted signal can be..
