论文标题
控制混乱的控制最少的信息传递
Control of chaos with minimal information transfer
论文作者
论文摘要
本文研究了离散时间控制系统的双曲线设置和稳定双曲线集的设置和稳定。我们首先研究双曲线集的结构和控制理论特性，特别是通过在不受控制的系统中添加小的控制项（经典）双曲线集来产生。然后，根据不稳定的体积生长速率和相关随机动力学系统的测量理论纤维熵之间的差异，我们在双曲线集的不变性熵上得出了一个下限。我们还证明，在两种极端情况下，我们的下限紧绷。此外，我们将技术应用于局部均匀稳定的问题，以屈曲。最后，我们讨论了建立在Hénon马蹄铁上的示例。
This paper studies set-invariance and stabilization of hyperbolic sets over rate-limited channels for discrete-time control systems. We first investigate structural and control-theoretic properties of hyperbolic sets, in particular such that arise by adding small control terms to uncontrolled systems admitting (classical) hyperbolic sets. Then we derive a lower bound on the invariance entropy of a hyperbolic set in terms of the difference between the unstable volume growth rate and the measure-theoretic fiber entropy of associated random dynamical systems. We also prove that our lower bound is tight in two extreme cases. Furthermore, we apply our techniques to the problem of local uniform stabilization to a hyperbolic set. Finally, we discuss an example built on the Hénon horseshoe.
