论文标题
扩展的Koopman模型
Extended Koopman Models
论文作者
论文摘要
我们介绍了非线性动态建模的Koopman操作员方法的两个新颖概括。这些概括中的每一个都会大大提高预测性能，而无需牺牲Koopman方法的独特特征：快速，全球最佳控制非线性，非凸系统的潜力。第一个概括是凸库曼模型，在提升空间中使用凸而不是线性动力学。第二个扩展的Koopman模型还引入了控制信号的可逆转换，这有助于凸起的凸动力学。我们描述了一个深度学习体系结构，用于参数化这些模型类别，并在实验上表明，在两个非线性，非convex动态系统的轨迹预测中，每个模型都显着优于传统的Koopman模型。
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the potential for fast, globally optimal control of nonlinear, nonconvex systems. The first generalization, Convex Koopman Models, uses convex rather than linear dynamics in the lifted space. The second, Extended Koopman Models, additionally introduces an invertible transformation of the control signal which contributes to the lifted convex dynamics. We describe a deep learning architecture for parameterizing these classes of models, and show experimentally that each significantly outperforms traditional Koopman models in trajectory prediction for two nonlinear, nonconvex dynamic systems.
