基于数据驱动的二次输出线性动力系统AAA建模
Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework
摘要：
我们扩展了AAA（自适应Antoulas-Anderson）算法，开发了一个数据驱动的二次输出线性系（LQO）建模框架。这种系统的特征在于两个传递函数：一个对应于输出的线性部分，另一个对应于二次部分。首先建立了LQO系统两个传递函数的联合重心表示和插值理论。这一分析导致提出AAA-LQO算法。我们表明，通过内插的传递函数值的一个子集上的样本施加一个最小二乘最小化的休息，我们构建可靠的数据驱动的LQO模型。两个数值算例说明了该方法的有效性。
英文摘要：
We extend the AAA (Adaptive-Antoulas-Anderson) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO). Such systems are characterized by two transfer functions: one corresponding to the linear part of the output and another one to the quadratic part. We first establish the joint barycentric representations and the interpolation theory for the two transfer functions of LQO systems. This analysis leads to the proposed AAA-LQO algorithm. We show that by interpolating the transfer function values on a subset of samples together with imposing a least-squares minimization on the rest, we construct reliable data-driven LQO models. Two numerical test cases illustrate the efficiency of the proposed method.
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