论文标题
平衡截断模型降低，具有非零初始值的LTI系统的先验误差界限
Balanced Truncation Model Reduction with A Priori Error Bounds for LTI Systems with Nonzero Initial Value
论文作者
论文摘要
在标准平衡截断模型降低中，通常在还原过程中忽略了初始条件，并且假定为零。但是，如果初始条件不是零，那么减少阶模型可能与全阶系统的近似值不佳。在文献中，有几次尝试以没有错误约束或仅一个后验错误界的价格进行修改的减少方法，通常太昂贵了，无法评估。在这项工作中，我们提出了一种基于对国家的转变转换的新平衡程序。我们首先得出一个联合投影降低的模型，其中系统的一部分仅取决于输入，而仅根据初始值进行了一次降低，我们证明了一个先验误差绑定。通过手头上的结果，我们得出了一个单独的投影过程，其中两个部分分别减少。这赋予了为不同子系统选择不同减少订单的自由。此外，我们讨论如何在实践中构建降级模型。由于误差界限是参数依赖性的，我们显示如何有效地优化它们。我们通过将我们的结果与文献的结果进行比较，通过一系列数值实验将我们的结果进行了比较。
In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order system, if the initial condition is not zero. In the literature there are several attempts for modified reduction methods at the price of having no error bound or only a posteriori error bounds which are often too expensive to evaluate. In this work we propose a new balancing procedure that is based on a shift transformation on the state. We first derive a joint projection reduced-order model in which the part of the system depending only on the input and the one depending only on the initial value are reduced at once and we prove an a priori error bound. With this result at hand, we derive a separate projection procedure in which the two parts are reduced separately. This gives the freedom to choose different reduction orders for the different subsystems. Moreover, we discuss how the reduced-order models can be constructed in practice. Since the error bounds are parameter-dependent we show how they can be optimized efficiently. We conclude this paper by comparing our results with the ones from the literature by a series of numerical experiments.
