论文标题
使用深度学习学习非线性动力学的线性表示
Learning Linear Representations of Nonlinear Dynamics Using Deep Learning
论文作者
论文摘要
绝大多数实践感兴趣系统的特征是非线性动力学。这使该系统的控制和优化由于其非线性行为而成为复杂的任务。另外，诸如固定点围绕固定点线性化的标准方法可能不是许多系统的有效策略，因此需要采用替代方法。因此，我们提出了一个新的深度学习框架，以发现非线性动力学系统对等效较高维度线性表示的转换。我们证明，与标准线性化相比，所得学习的线性表示能够准确地捕获原始系统的动力学。结果，我们表明，学习的线性模型随后可以用于成功控制原始系统。我们通过将提出的框架应用于两个示例来证明这一点。一个来自文献和更复杂的示例，形式是连续搅拌罐反应器（CSTR）。
The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as linearizing around a fixed point may not be an effective strategy for many systems, thus requiring an alternative approach. For this reason, we propose a new deep learning framework to discover a transformation of a nonlinear dynamical system to an equivalent higher dimensional linear representation. We demonstrate that the resulting learned linear representation accurately captures the dynamics of the original system for a wider range of conditions than standard linearization. As a result of this, we show that the learned linear model can subsequently be used for the successful control of the original system. We demonstrate this by applying the proposed framework to two examples; one from the literature and a more complex example in the form of a Continuous Stirred Tank Reactor (CSTR).
