Adaptive A-Optimal Experimental Design for Linear Dynamical Systems
Adaptive A-Optimal Experimental Design for Linear Dynamical Systems
复制标题
线性动力系统的自适应 A 最优实验设计
DOI：
10.1137/15m1034738
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
E. Haber
中科院分区：
文献类型：
--
作者：
J. Fohring;E. Haber
虽然静态线性逆问题的最优实验设计已经得到了很好的研究，但很少有动态系统的实验设计方法-特别是动态问题，其中最优实验设计方法包括历史数据，使得实验跟踪模型的运动。因此，我们提出了一种自适应设计方法，它最小化正则化模型估计的自适应均方误差，该方法通过引入监视函数来定义，该监视函数根据历史模型估计来缩放均方误差。根据动态过程中误差的分类，提出了两种模型估计公式的自适应设计方法。首先，我们考虑动力系统不存在误差的情况，将反问题转化为一个偏微分方程组约束优化问题，以恢复初始条件。其次，我们考虑了动力学中的误差，并将逆问题表示为卡尔曼平滑系统，以记录系统的动态特性。
While optimal experimental design for static linear inverse problems has been well studied, there is little in the way of experimental design methods for dynamical systems---in particular, dynamic problems where historic data is included in the optimal experimental design method such that the experiment tracks the motion of the model. Thus, we propose an adaptive design method which minimizes the adapted mean squared error of the regularized model estimate, defined by introducing a monitor function which scales the mean squared error according to historic model estimates. We present the adaptive design method for two model estimation formulations based on the classification of the error in the dynamic process. First, we consider the case where there is no error in the dynamical system and formulate the inverse problem as a PDE constrained optimization problem to recover the initial condition. Second, we include the error in the dynamics and formulate the inverse problem as a Kalman smoothing system to rec...