论文标题
控制动态的拓扑必要条件
Topological Necessary Conditions for Control Dynamics
论文作者
论文摘要
给出了具有指定拓扑类型的吸引子的受控动力学的必要条件的分析。它对歧管的高斯图使用HOPF分类来实现相同维度的球体，在这种情况下，通过线性同型，对于Lyapunov函数的梯度流量和稳定矢量场的梯度流量，程度相同。这些歧管是Lyapunov级别集。通过考虑同源性地图给出更一般的环境。一些帐户是对学位为零且溢流力失败的情况。这项工作的一个版本于2009年提交出版，目前正在修订和扩展过程中。
An analysis of necessary conditions for the existence of controlled dynamics with an attractor of a specified topological type is given. It uses the Hopf classification by degree for Gauss maps of manifolds to spheres of the same dimension, in this case noting that by a linear homotopy, the degree is the same for the negative of the gradient flow of a Lyapunov function and for the stabilising vector field. The manifolds are Lyapunov level sets. More general contexts are given by considering maps in homology. Some account is taken of cases where the degree is zero and the surjectivity fails. A version of this work was submitted for publication in 2009, and the paper is now in the process of revision and expansion.
