稳定不稳定或混沌映射的随机控制
Stochastic control stabilizing unstable or chaotic maps
摘要：
本文研究了一种稳定化的随机控制，它可以应用于各种不稳定甚至混沌映射。与以前引入噪声控制的方法相比，我们放松了对映射类的假设，并考虑了相同映射的更宽范围的参数。这种方法允许通过噪声稳定不稳定和混沌映射。地图属性和允许的解决方案可以开始稳定的邻域之间的相互作用进行了探讨：作为不稳定的原始地图的增加，允许的初始条件的间隔变窄。一个有向随机控制，旨在获得目标的邻域几乎必然与控制噪声相结合。仿真结果表明，对于各种问题，适当的有界噪声可以稳定一个不稳定的正平衡点，而不限制的初始值。
英文摘要：
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as consider a wider range of parameters for the same maps. This approach allows to stabilize unstable and chaotic maps by noise. The interplay between the map properties and the allowed neighbourhood where a solution can start to be stabilized is explored: as instability of the original map increases, the interval of allowed initial conditions narrows. A directed stochastic control aiming at getting to the target neighbourhood almost sure is combined with a controlling noise. Simulations illustrate that for a variety of problems, an appropriate bounded noise can stabilize an unstable positive equilibrium, without a limitation on the initial value.
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