新多涡卷混沌系统的控制与同步
发布时间：2018-09-05 13:45
【摘要】：多涡卷混沌系统与双涡卷混沌系统相比其动力学行为、拓扑结构以及密匙参数更复杂,多涡卷混沌系统广泛的应用于混沌系统的信息加密中,目前多涡卷混沌系统的产生主要在于构造适当的非线性函数产生多涡卷混沌系统,但对多涡卷混沌系统的混沌特性分析不够充分。由于多涡卷混沌系统的分析难以用传统的动力学理论分析,传统的控制理论较难对多涡卷混沌系统进行控制研究,因此国内外对多涡卷混沌系统的分析研究的文献较少。但多涡卷混沌系统的控制与同步研究对于工程应用具有重要理论意义和应用价值,将多涡卷混沌系统应用到工程领域具有很大的发展前景。本文在Jerk系统的基础上通过由分段线性函数所组成的非线性函数产生多涡卷混沌系统,与双涡卷Jerk系统相比增加了系统在单方向的涡卷数,从而增加了混沌系统的复杂性,数值计算了新多涡卷混沌系统的散度、平衡点、Lyapunov指数、Lyapunov维数的值,并对其Lyapunov指数谱和分岔图进行了基本动力学分析,数值模拟体现了系统的多涡卷特性,电路实验证明了新系统的物理可实现性。同时采用非线性反馈法、滑模变结构控制法、线性反馈滑模控制法对新多涡卷混沌系统进行了追踪控制,与非线性反馈法、滑模变结构控制法相比,线性反馈滑模控制法缩短了新多涡卷混沌系统对目标信号的追踪时间,提高了追踪效率,数值模拟和电路实验说明了这三种控制方法均可实现新多涡卷混沌系统对参考信号的追踪目标。最后采用主动控制法和主动滑模控制法、自适应滑模控制法、线性反馈控制法和线性反馈滑模控制法对新多涡卷混沌系统进行了同步研究,主动滑模控制法与主动控制法相比明显缩短了驱动系统与响应系统到达同步的时间,但主动滑模控制法的控制器比较复杂,而自适应滑模控制法与主动滑模控制法相比同样可使两系统达到同步,且简化了控制器的复杂度,线性反馈控制法物理实验易于实现,但达到同步的时间较长,鲁棒性较弱,线性反馈滑模控制法与主动滑模控制法及自适应滑模控制法相比,极大的缩短了两系统到达同步的时间,提高了同步效果,且与线性反馈法相比,具有较强的抗干扰能力,鲁棒性较高。
[Abstract]:The dynamical behavior, topology and key parameters of multi-scroll chaotic system are more complex than that of double-scroll chaotic system. Multi-scroll chaotic system is widely used in information encryption of chaotic system. At present, the generation of multi-scroll chaotic system mainly lies in the construction of proper nonlinear function to produce multi-scroll chaotic system, but the chaotic characteristics of multi-scroll chaotic system are not sufficiently analyzed. Because the analysis of multi-scroll chaotic system is difficult to be analyzed by the traditional dynamics theory and the traditional control theory is difficult to control the multi-scroll chaotic system, there are few literatures on the analysis and research of multi-scroll chaotic system at home and abroad. However, the research on the control and synchronization of multi-scroll chaotic systems is of great theoretical significance and application value for engineering applications, and the application of multi-scroll chaotic systems to the engineering field has a great development prospect. On the basis of the Jerk system, a multi-scroll chaotic system is generated by a nonlinear function composed of piecewise linear functions. Compared with the two-scroll Jerk system, the number of vortexes in one direction is increased and the complexity of the chaotic system is increased. The divergence and the Lyapunov exponent dimension of the new multi-scroll chaotic system are numerically calculated, and the Lyapunov exponent spectrum and bifurcation diagram are analyzed. The numerical simulation shows the multi-vorticity characteristic of the system. The circuit experiment proves the physical realizability of the new system. At the same time, nonlinear feedback method, sliding mode variable structure control method and linear feedback sliding mode control method are used to track control the new multi-scroll chaotic system, compared with nonlinear feedback method and sliding mode variable structure control method. The linear feedback sliding mode control method shortens the tracking time of the new multi-scroll chaotic system and improves the tracking efficiency. Numerical simulation and circuit experiments show that these three control methods can achieve the tracking target of the reference signal in the new multi-scroll chaotic system. Finally, active control method, active sliding mode control method, adaptive sliding mode control method, linear feedback control method and linear feedback sliding mode control method are used to synchronize the new multi-scroll chaotic system. Compared with the active control method, the active sliding mode control method obviously shortens the time between the drive system and the response system, but the controller of the active sliding mode control method is more complex. Compared with the active sliding mode control, the adaptive sliding mode control method can make the two systems synchronize, and simplify the complexity of the controller. The linear feedback control method is easy to realize in physical experiments, but the synchronization time is longer and the robustness is weak. Compared with the active sliding mode control and the adaptive sliding mode control, the linear feedback sliding mode control method can greatly shorten the time between the two systems to achieve synchronization and improve the synchronization effect. Compared with the linear feedback control method, the linear sliding mode control method has stronger anti-interference ability. The robustness is high.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;TP13
本文编号：2224452
[Abstract]:The dynamical behavior, topology and key parameters of multi-scroll chaotic system are more complex than that of double-scroll chaotic system. Multi-scroll chaotic system is widely used in information encryption of chaotic system. At present, the generation of multi-scroll chaotic system mainly lies in the construction of proper nonlinear function to produce multi-scroll chaotic system, but the chaotic characteristics of multi-scroll chaotic system are not sufficiently analyzed. Because the analysis of multi-scroll chaotic system is difficult to be analyzed by the traditional dynamics theory and the traditional control theory is difficult to control the multi-scroll chaotic system, there are few literatures on the analysis and research of multi-scroll chaotic system at home and abroad. However, the research on the control and synchronization of multi-scroll chaotic systems is of great theoretical significance and application value for engineering applications, and the application of multi-scroll chaotic systems to the engineering field has a great development prospect. On the basis of the Jerk system, a multi-scroll chaotic system is generated by a nonlinear function composed of piecewise linear functions. Compared with the two-scroll Jerk system, the number of vortexes in one direction is increased and the complexity of the chaotic system is increased. The divergence and the Lyapunov exponent dimension of the new multi-scroll chaotic system are numerically calculated, and the Lyapunov exponent spectrum and bifurcation diagram are analyzed. The numerical simulation shows the multi-vorticity characteristic of the system. The circuit experiment proves the physical realizability of the new system. At the same time, nonlinear feedback method, sliding mode variable structure control method and linear feedback sliding mode control method are used to track control the new multi-scroll chaotic system, compared with nonlinear feedback method and sliding mode variable structure control method. The linear feedback sliding mode control method shortens the tracking time of the new multi-scroll chaotic system and improves the tracking efficiency. Numerical simulation and circuit experiments show that these three control methods can achieve the tracking target of the reference signal in the new multi-scroll chaotic system. Finally, active control method, active sliding mode control method, adaptive sliding mode control method, linear feedback control method and linear feedback sliding mode control method are used to synchronize the new multi-scroll chaotic system. Compared with the active control method, the active sliding mode control method obviously shortens the time between the drive system and the response system, but the controller of the active sliding mode control method is more complex. Compared with the active sliding mode control, the adaptive sliding mode control method can make the two systems synchronize, and simplify the complexity of the controller. The linear feedback control method is easy to realize in physical experiments, but the synchronization time is longer and the robustness is weak. Compared with the active sliding mode control and the adaptive sliding mode control, the linear feedback sliding mode control method can greatly shorten the time between the two systems to achieve synchronization and improve the synchronization effect. Compared with the linear feedback control method, the linear sliding mode control method has stronger anti-interference ability. The robustness is high.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;TP13
【参考文献】
相关期刊论文 前10条
1 杨志昌;李虹;张波;吕金虎;;基于多涡卷混沌吸引子的电力电子变换器混沌PWM控制研究[J];电源学报;2017年03期
2 边潇俊;林达;谢玉姣;;基于滑膜控制和SAFNN的鲁棒混沌同步[J];四川理工学院学报(自然科学版);2015年05期
3 潘光;魏静;;一种分数阶混沌系统同步的自适应滑模控制器设计[J];物理学报;2015年04期
4 孙克辉;艾星星;左婷;朱从旭;;多涡卷Chua混沌吸引子的设计与性能分析[J];动力学与控制学报;2015年01期
5 仲启龙;邵永晖;郑永爱;;分数阶混沌系统的主动滑模同步[J];动力学与控制学报;2015年01期
6 陈娇英;彭宇宁;唐英姿;;双涡卷Jerk非线性系统混沌电路设计[J];桂林理工大学学报;2015年01期
7 李洁;黄艳宾;石丁丁;杨静;卢建敏;;多涡卷混沌系统的有限时间滑模控制[J];科技通报;2015年01期
8 徐瑞萍;高存臣;;基于线性反馈控制的一类混沌系统的同步[J];中国海洋大学学报(自然科学版);2014年05期
9 刘明华;;多涡卷四阶Jerk系统的仿真研究[J];井冈山大学学报(自然科学版);2013年04期
10 曹鹤飞;张若洵;;基于单驱动变量分数阶混沌同步的参数调制数字通信及硬件实现[J];物理学报;2012年02期
相关博士学位论文 前3条
1 孙光辉;分数阶混沌系统的控制及同步研究[D];哈尔滨工业大学;2010年
2 闵富红;混沌系统同步控制的有关问题研究[D];南京理工大学;2007年
3 孙克辉;混沌同步控制理论及其在信息加密中的应用研究[D];中南大学;2005年
，本文编号：2224452
本文链接：https://www.wllwen.com/kejilunwen/zidonghuakongzhilunwen/2224452.html
