论文标题
pyragas对离散波的控制
Equivariant Pyragas control of discrete waves
论文作者
论文摘要
pyragas控制是一种延迟的反馈方法，旨在稳定具有对称性的系统中的时空模式。在本文中，我们将epyragas Control应用于离散波，这些波浪是具有有限数量时空对称性的周期性解决方案。我们证明了足够的条件，在该条件下，可以通过pyragas控制能够稳定离散波。结果不适用于广泛的离散波，包括离分叉点很远的离散波。证明的关键要素是将浮球理论适应具有对称性的系统，以及使用特征矩阵函数将无限尺寸特征值问题减少到一个维度零查找问题。
Equivariant Pyragas control is a delayed feedback method that aims to stabilize spatio-temporal patterns in systems with symmetries. In this article, we apply equivariant Pyragas control to discrete waves, which are periodic solutions that have a finite number of spatio-temporal symmetries. We prove sufficient conditions under which a discrete wave can be stabilized via equivariant Pyragas control. The result isapplicable to a broad class of discrete waves, including discrete waves that are far away from a bifurcation point. Key ingredients of the proof are an adaptation of Floquet theory to systems with symmetries, and the use of characteristic matrix functions to reduce the infinite dimensional eigenvalue problem to a one dimensional zero finding problem.
