Control of chaos by occasional bang-bang.
Control of chaos by occasional bang-bang.
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DOI：
10.1103/physreve.67.036203
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发表时间：
2003-03
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通讯作者：
J. Starrett
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作者：
J. Starrett
奇异吸引子中周期性鞍形轨道（目标轨道）的稳定通常是通过应用一系列参数扰动来实现的，这些参数扰动旨在将系统状态置于目标的稳定流形中，从而不受扰动地演化到目标轨道。这种类型的控制起源于 Ott、Grebogi 和 Yorke (OGY) 的方法，通常需要连续可变的参数来进行基于地图的控制。 Bang-bang 控制是一种通过应用固定或几个不同的固定扰动而不是连续范围的扰动来实现控制的方法，并且通常需要灵活的调度。如果我们只有固定的扰动水平，并且只能在固定的时间间隔和固定的持续时间内应用控制，那么标准 OGY 将不起作用。我们演示了一种方法，可以通过固定持续时间的单个固定扰动来控制剖面表面的地图和连续系统，尽管不精确。我们称这种情况为“偶尔的爆炸”。
The stabilization of a periodic saddle orbit (the target orbit) in a strange attractor is usually achieved by the application of a sequence of parameter perturbations designed to place the system state in the stable manifold of the target, whereupon it evolves unperturbed to the target orbit. Controls of this type originated with the method of Ott, Grebogi, and Yorke (OGY), and usually require a continuously variable parameter for map based control. Bang-bang control is a method whereby control is achieved by the application of a fixed, or several different fixed perturbations, rather than a continuous range of perturbations, and generally requires a flexible scheduling. If we have available only fixed perturbation levels, and can apply control only at regular intervals and for fixed durations, standard OGY will not work. We demonstrate a method that will control maps and continuous systems at a surface of section, albeit imprecisely, with a single fixed perturbation of fixed duration. We call this occasional bang bang.