端口哈密顿系统模型降阶的保结构切向内插
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
AI总结：
针对大规模多输入多输出端口哈密顿系统，提出通过切向有理插值进行模型降阶，所得降阶模型保持端口哈密顿结构且无源，并引入基于H2最优的算法选择插值点与切向方向。
摘要：
端口哈密顿系统源于基于端口的物理系统网络建模，是无源状态空间系统的重要实例。本文发展了通过切向有理插值对大规模多输入/多输出端口哈密顿系统进行模型降阶的框架。所得降阶模型不仅是切向有理插值函数，而且保留了端口哈密顿结构，因此是无源的。该降阶方法在能量和协能量系统坐标中均有描述。我们还引入了一种受$\mathcal{H}_2$启发的算法，用于有效选择插值点和切向方向。该算法得到的降阶端口哈密顿模型满足$\mathcal{H}_2$最优条件的一个子集。我们给出了几个数值例子，说明了所提方法的有效性，表明其在质量和数值效率上均优于现有其他技术。
英文摘要：
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale multi-input/multi-output port-Hamiltonian systems via tangential rational interpolation. The resulting reduced-order model not only is a rational tangential interpolant but also retains the port-Hamiltonian structure; hence is passive. This reduction methodology is described in both energy and co-energy system coordinates. We also introduce an $\mathcal{H}_2$-inspired algorithm for effectively choosing the interpolation points and tangential directions. The algorithm leads a reduced port-Hamiltonian model that satisfies a subset of $\mathcal{H}_2$-optimality conditions. We present several numerical examples that illustrate the effectiveness of the proposed method showing that it outperforms other existing techniques in both quality and numerical efficiency.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
