Chaos control based on stability Transformation method for unstable periodic orbits
Chaos control based on stability Transformation method for unstable periodic orbits
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DOI：
10.1587/nolta.3.246
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Yuki Kawai;T. Tsubone
中科院分区：
文献类型：
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作者：
Yuki Kawai;T. Tsubone
为了检测具有混沌行为的动力系统中不稳定周期轨道的位置，提出了稳定性变换方法。基于该方法的混沌控制方法也已被考虑。混沌控制方法可以稳定未知的稳态，但控制方法使用对应于长度为l的周期轨道的l次迭代Poincare映射。因此，存在与鲁棒性相关的缺点，并且需要对控制方法的实现进行更详细的讨论。提出了一种基于稳定性变换的不稳定周期轨道混沌控制方法。该方法可以镇定状态未知的不稳定周期轨道。我们表明，我们的方法有一个更广泛的控制参数范围，以保证稳定性比以前的方法，可以实现一个简单的电路实现。文中给出了一些算例，并通过实验室测量证实了理论结果。
Stability transformation method has been proposed in order to detect the location of a unstable periodic orbit in a dynamical system which exhibits chaotic behavior. A chaos control approach based on the method has been also considered. The chaos control method can stabilize unknown steady states, however the control method uses l-times iterated Poincare map corresponding to a periodic orbit of length l. Therefore there is a disadvantage related to robustness and more detailed discussion for realization of the control method is needed. In this paper, we propose a novel chaos control method based on stability transformation method for unstable periodic orbits. The method can stabilize unstable periodic orbits whose states are unknown. We show that our method has a much wider range of control parameters to guarantee stability than ones of a previous method and can be realized by a simple circuit implementation. Some examples are provided and the some theoretical results are confirmed by laboratory measurements.