论文标题
Koopman期望：一种经营者理论方法，用于有效分析和优化不确定的混合动力学系统
The Koopman Expectation: An Operator Theoretic Method for Efficient Analysis and Optimization of Uncertain Hybrid Dynamical Systems
论文作者
论文摘要
对于涉及决策的动态系统，系统的成功在很大程度上取决于其使用不完整和不确定的信息做出良好决策的能力。通过利用Koopman操作员及其伴随属性，我们介绍了Koopman的期望，这是一种通过动态系统传播的计算期望的有效方法。与文献中基于Koopman运营商的其他方法不同，这是可能的，没有Koopman操作员的明确表示。此外，当考虑到预期损失和约束时，在不确定性下，将利用Koopman期望提高的效率进行优化。我们展示了Koopman的期望如何适用于具有非高斯初始条件和参数不确定性的过程噪声驱动的离散，连续和混合非线性系统。我们通过演示1700倍的加速度来计算在幼稚的蒙特卡洛方法上杂种动力学系统的概率量，其准确性的大幅度提高了。
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we introduce the Koopman Expectation, an efficient method for computing expectations as propagated through a dynamical system. Unlike other Koopman operator-based approaches in the literature, this is possible without an explicit representation of the Koopman operator. Furthermore, the efficiencies enabled by the Koopman Expectation are leveraged for optimization under uncertainty when expected losses and constraints are considered. We show how the Koopman Expectation is applicable to discrete, continuous, and hybrid non-linear systems driven by process noise with non-Gaussian initial condition and parametric uncertainties. We finish by demonstrating a 1700x acceleration for calculating probabilistic quantities of a hybrid dynamical system over the naive Monte Carlo approach with many orders of magnitudes improvement in accuracy.
