论文标题
通过运营商理论指标生成不确定性的MCMC方法
An MCMC Method for Uncertainty Set Generation via Operator-Theoretic Metrics
论文作者
论文摘要
在许多可靠的优化问题中，需要模型不确定性集，例如具有不确定性的可靠控制和预测，但是没有确定的方法可以为非线性动力学系统生成不确定性集。在本文中，我们提出了一种通过Markov Chain Monte Carlo建模不确定性集的方法。通过转移运算符上的指标，来自动态系统的分布中提出的方法样本，适用于一般的非线性系统。我们以计算有效的方式适应了哈密顿蒙特卡洛（Hamiltonian Monte Carlo）来对高维转移操作员进行采样。我们提出数值示例，以验证提出的不确定性设置生成的方法。
Model uncertainty sets are required in many robust optimization problems, such as robust control and prediction with uncertainty, but there is no definite methodology to generate uncertainty sets for nonlinear dynamical systems. In this paper, we propose a method for model uncertainty set generation via Markov chain Monte Carlo. The proposed method samples from distributions over dynamical systems via metrics over transfer operators and is applicable to general nonlinear systems. We adapt Hamiltonian Monte Carlo for sampling high-dimensional transfer operators in a computationally efficient manner. We present numerical examples to validate the proposed method for uncertainty set generation.
