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The Information Matrix in Control: Computation and Some Applications

机译:控制中的信息矩阵:计算和一些应用

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摘要

The Fisher information matrix plays a central role in estimation and input design for input-output systems. This matrix provides a summary of the amount of information in the data relative to the quantities of interest. Some of the specific applications of the information matrix include confidence region calculation for parameter estimates, the determination of optimal inputs for model building, the providing of a bound on the best possible performance in an adaptive system (such as a control system), and producing uncertainty bounds on predictions (such as with a neural network). Unfortunately, the analytical calculation of the information matrix is often a difficult or impossible task. This is especially the case with nonh'near models such as neural networks. This paper will briefly review some of the applications of the information matrix in control and describe a resampling-based method for computing the information matrix. This method applies in problems of arbitrary difficulty and is relatively easy to implement.
机译:Fisher信息矩阵在输入输出系统的估计和输入设计中起着核心作用。该矩阵提供了数据中相对于感兴趣量的信息量的摘要。信息矩阵的某些特定应用包括参数估计的置信区域计算,用于模型构建的最佳输入的确定,在自适应系统(例如控制系统)中提供最佳性能的界限,以及产生预测的不确定性范围(例如神经网络)。不幸的是,信息矩阵的分析计算通常是困难或不可能的任务。对于非近距离模型(例如神经网络)尤其如此。本文将简要回顾一下信息矩阵在控制中的一些应用,并介绍一种基于重采样的信息矩阵计算方法。该方法适用于任意困难的问题,并且相对容易实现。

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