| Lauwerier映射的混沌控制 |
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| 引用本文： | 郭峰,谢建华,乐源.Lauwerier映射的混沌控制[J].西南交通大学学报,2014,27(3):525-529. |
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| 作者姓名： | 郭峰 谢建华 乐源 |
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| 基金项目： | 国家自然科学基金资助项目（11172246，11272268）中央高校基本科研业务费专项资金资助项目（SWJTU11ZT15） |
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| 摘 要： | 为了克服混沌控制外加激励或阻尼的方法在控制过程中改变了原系统动力学行为的缺陷，将OGY混沌控制方法与线性控制理论极点配置法相结合，建立了线性化映射，利用极点配置法选择依赖时间变化的控制参数的小扰动，提出了对Lauwerier映射的混沌运动进行控制的新方法.根据混沌运动的遍历性，在吸引子中嵌入不稳定的周期轨道，选取不稳定的周期-1和周期-2轨道作为控制目标，当相点运动到这些周期轨道附近时，对控制参数进行微小扰动，将不稳定轨道控制在相应的稳定轨道上，并分析了不同调节器极点对混沌控制时间的影响.研究结果表明:当两个极点分别取1/8和0时，系统经过230次迭代将不稳定的轨道控制在不动点；当两个极点分别取1/6和-1/4时，经过3 300次迭代才能实现混沌控制；该方法在混沌控制的过程中没有改变原系统的动力学性质.
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| 关 键 词： | Lauwerier映射 混沌吸引子 混沌控制 极点配置 |
| 收稿时间： | 2012-05-22 |
Chaos Control of Lauwerier Mapping |
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| GUO Feng,XIE Jianhua,YUE Yuan.Chaos Control of Lauwerier Mapping[J].Journal of Southwest Jiaotong University,2014,27(3):525-529. |
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| Authors: | GUO Feng XIE Jianhua YUE Yuan |
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| Abstract: | In order to overcome the defect that the properties of the original system is changed in the process of chaos control with external excitation or damping, the OGY control method is combined with the pole placement technique of the linear control theory to establish a linear mapping. By applying the pole placement technique to select a small time-dependent perturbation of the control parameter, a new method is proposed to control the chaos movement of Lauwerier mapping. According to the ergodicity of chaos movement, the unstable periodic orbits are embedded into the chaotic attractor. The unstable period-1 and period-2 orbits are selected as the control targets. When map points wander to the neighborhood of these periodic orbits, a small perturbation is added to the system control parameter, and the unstable period-1 and period-2 orbits are controlled to be stable. In addition, the influence of different regulator poles on the control time is analyzed. The results show that when the two poles are 1/8 and 0, respectively, the unstable period-1 orbit is controlled at the fixed point after 230 iterations; and when the two poles are 1/6 and -1/4, the chaos control is achieved after 3 300 iterations. The dynamic properties of the original system is not changed in the process of the chaos control. |
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