论文标题
部分可观测时空混沌系统的无模型预测
Distance problems for dissipative Hamiltonian systems and related matrix polynomials
论文作者
论文摘要
我们研究了具有耗散性的哈密顿结构的线性差分 - 代数系统的几个距离问题的表征。由于所有模型只是现实的近似值，并且数据总是不准确，因此给定模型是否接近可以被视为不稳定或单数的“不良”模型，这是一个重要的问题。这通常是通过计算具有此类属性最近模型的距离来完成的。我们将讨论与奇异性的距离以及与耗散哈密顿系统最近高指数问题的距离。尽管对于一般的非结构化差分 - 代数系统，这些距离的表征是部分开放的问题，但我们将证明，对于耗散性的汉密尔顿系统和相关的矩阵多项式，存在明确的特征，可以数值实现。
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an important question whether a given model is close to a 'bad' model that could be considered as ill-posed or singular. This is usually done by computing a distance to the nearest model with such properties. We will discuss the distance to singularity and the distance to the nearest high index problem for dissipative Hamiltonian systems. While for general unstructured differential-algebraic systems the characterization of these distances are partially open problems, we will show that for dissipative Hamiltonian systems and related matrix polynomials there exist explicit characterizations that can be implemented numerically.
