论文标题
部分可观测时空混沌系统的无模型预测
Doubly structured mapping problems of the form $Δx=y$ and $Δ^*z=w$
论文作者
论文摘要
对于给定类的结构化矩阵$ \ mathbb s $，我们在vectors $ x，w \ in \ c^{n+m} $和$ y，z \ in \ c^{n} $中$δ= [δ_1〜Δ_2] $ uncy $Δ_1$ unt \ c^{ \ c^{n，m} $，这样$ΔX= y $和$Δ^*z = w $。我们还表征了所有此类映射$δ$的集合，并为向量$ x，y，z $和$ w $提供足够的条件，以调查使用最小的Frobenius Norm的$δ$。我们考虑的结构化类$ \ mathbb s $包括（倾斜）-hermitian，（skew） - 米对称，伪（skew）-symmetric，$ j $ - （skew）-symmetric，pseudo（skew）-hermitian，-mermitian，阳性（阳性（semi）（semi）（semi）（semi）和indusip and umplice and umplice and umplice and uspunip and indusip and indusip。然后，这些映射用于计算最佳控制中产生的基质铅笔的结构化特征值/特征pair的向后误差。
For a given class of structured matrices $\mathbb S$, we find necessary and sufficient conditions on vectors $x,w\in \C^{n+m}$ and $y,z \in \C^{n}$ for which there exists $Δ=[Δ_1~Δ_2]$ with $Δ_1 \in \mathbb S$ and $Δ_2 \in \C^{n,m}$ such that $Δx=y$ and $Δ^*z=w$. We also characterize the set of all such mappings $Δ$ and provide sufficient conditions on vectors $x,y,z$, and $w$ to investigate a $Δ$ with minimal Frobenius norm. The structured classes $\mathbb S$ we consider include (skew)-Hermitian, (skew)-symmetric, pseudo(skew)-symmetric, $J$-(skew)-symmetric, pseudo(skew)-Hermitian, positive (semi)definite, and dissipative matrices. These mappings are then used in computing the structured eigenvalue/eigenpair backward errors of matrix pencils arising in optimal control.
