We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without reference to any prescribed realization of the original model. Data are represented by sampled values of the transfer function {or the impulse response} corresponding to the original model. We discuss parallels that our approach bears with the Loewner framework, another popular data-driven model reduction method. We illustrate our approach numerically in both continuous-time and discrete-time cases.
翻译:我们提出了一个平衡脱节的新版本,这是一种典型的典型的减少模式方法。我们引入的主要创新是通过使用系统反应数据,这些数据已经测量或计算,没有参考原始模型的任何规定实现情况。数据代表的是与原始模型相对应的转移函数{或冲动反应}的抽样值。我们讨论了我们的方法与Lewner框架的平行之处,这是另一个流行的数据驱动模式减少方法。我们在连续时间和离散时间案例中都用数字来说明我们的方法。