论文标题
通过安全函数控制二维混沌瞬变
Controlling two-dimensional chaotic transients with the safety function
论文作者
论文摘要
在这项工作中，我们与Hénon和Lozi地图打交道，以选择它们显示瞬态混乱的参数。靠近混乱的马鞍的轨道在一段时间内表现出一段时间，最终逃到了外部吸引子上。传统上，为了防止这种逃脱，采用了部分控制技术。这种方法在考虑影响地图的干扰（噪声）和找到所谓的安全集的特殊区域的干扰（噪声）方面突出，该区域被称为安全集，而维持轨道所需的控制很小。但是，在这项工作中，我们将采用最近开发的部分控制方法的新方法。这种新方法基于找到一个称为安全功能的特殊功能，该功能可以自动找到避免轨道逃逸所需的最小控制。此外，我们将展示安全功能与经典安全集之间的牢固联系。为了说明这一点，我们将首次计算，对二维Hénon和Lozi地图的安全功能，在这里我们还显示了该功能的强烈依赖性，其影响地图的干扰幅度以及该变化如何极大地影响受控的轨道。
In this work we deal with the Hénon and the Lozi map for a choice of parameters where they show transient chaos. Orbits close to the chaotic saddle behave chaotically for a while to eventually escape to an external attractor. Traditionally, to prevent such an escape, the partial control technique has been applied. This method stands out for considering disturbances (noise) affecting the map and for finding a special region of the phase space, called the safe set, where the control required to sustain the orbits is small. However, in this work we will apply a new approach of the partial control method that has been recently developed. This new approach is based on finding a special function called the safety function, which allows to automatically find the minimum control necessary to avoid the escape of the orbits. Furthermore, we will show the strong connection between the safety function and the classical safe set. To illustrate that, we will compute for the first time, safety functions for the two-dimensional Hénon and Lozi maps, where we also show the strong dependence of this function with the magnitude of disturbances affecting the map, and how this change drastically impacts the controlled orbits.
