论文标题
通过哈密顿特征值优化查找最近的被动或非据点系统
Finding the nearest passive or non-passive system via Hamiltonian eigenvalue optimization
论文作者
论文摘要
我们提出并研究了一种用于计算给定非据线性时间流动系统最近的被动系统的算法（在选择定义“最近”的指标选择时具有很大的自由度，这可能仅限于结构化的扰动），也仅限于结构化的扰动），也可以将相关的算法计算为给定的被动系统的结构性距离到非passitive to Intraginal to Intraginal to Intraginal to not passitive to Intraginal to not passitive to Intraginal to not-Passitive。通过解决由扰动系统矩阵构建的哈密顿矩阵的特征值优化问题来解决这两个问题。所提出的算法是使用约束梯度流的固定尺寸的最小正实际部分优化最小正实数的哈密顿特征值的两级方法。他们在外迭代中的扰动大小上优化了，在典型的情况下，简单特征值接近想象轴的典型情况下，该迭代的扰动大小是四次收敛的。对于大型系统，我们提出了算法的一种变体，该算法利用了问题的固有低级结构。数值实验说明了提出的算法的行为。
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured perturbations), and also a closely related algorithm for computing the structured distance of a given passive system to non-passivity. Both problems are addressed by solving eigenvalue optimization problems for Hamiltonian matrices that are constructed from perturbed system matrices. The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow. They optimize over the perturbation size in the outer iteration, which is shown to converge quadratically in the typical case of a defective coalescence of simple eigenvalues approaching the imaginary axis. For large systems, we propose a variant of the algorithm that takes advantage of the inherent low-rank structure of the problem. Numerical experiments illustrate the behavior of the proposed algorithms.
