AI 中文总结
本文提出围道积分方法（CIM），将其与基于投影的模型降阶（MOR）结合，构建贪心算法及满足厄米特插值的投影框架，在基准控制系统上验证了该方法的精度与效率，降低了参数系统输入输出关系的评估成本。
AI 中文摘要
本文提出一种围道积分方法（CIM），用于在指定时间区间内以用户规定的精度高效计算控制形式下参数线性系统的输出。该方法通过沿修正积分围道应用求积规则来近似拉普拉斯逆变换。针对参数系统，本文展示了CIM如何与基于投影的模型降阶（MOR）有效结合，其中贪心算法遵循本文为该场景推导的误差估计构建投影空间。本文还证明，所开发的投影框架自然满足厄米特插值条件。这种组合大幅降低了跨参数域评估输入输出关系的成本，适用于广泛的输入函数以及低维子空间能良好捕获的初始条件。本文在基准非参数和参数控制系统上验证了该方法的精度与效率，并与最先进的基于投影的MOR方法进行了比较。
英文摘要
This paper introduces a contour integral method (CIM) for efficiently computing outputs of parametric linear systems in control form over specified time intervals and to a user-prescribed accuracy. The CIM approximates the inverse Laplace transform via a quadrature rule applied along a modified integration contour. For parametric systems, we show how CIM integrates effectively with projection-based model order reduction (MOR) where a greedy algorithm builds the projection spaces following an error estimate we derive for this setting. We additionally demonstrate that the developed projection framework naturally enforces Hermite interpolation conditions. This combination substantially lowers the cost of evaluating the input-output relations across the parameter domain, for a wide range of input functions, and for initial conditions well captured by a low-dimensional subspace.. We demonstrate the accuracy and efficiency of the approach on benchmark non-parametric and parametric control systems, comparing against state-of-the-art projection-based MOR methods.
