In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that every discrete-time nonlinear contracting model can be learnt in our framework. Another significant merit of the proposed approach is that it allows for unconstrained optimization over the Koopman embedding and operator jointly while enforcing stability of the model, via a direct parameterization of stable linear systems, greatly simplifying the computations involved. We validate our method on a simulated system and analyze the advantages of our parameterization compared to alternatives.
翻译:在本文中,我们展示了一种新的数据驱动方法,用于学习非线性系统的稳定模型。我们的模型利用Koopman嵌入器将原来的状态空间提升到一个高维线性元体。有趣的是,我们证明每一个离散时间的非线性订约模式都可以在我们的框架内学习。拟议方法的另一个重要优点是,它允许对库普曼嵌入和操作者联合进行不受限制的优化,同时通过稳定线性系统的直接参数化来稳定模型,大大简化了所涉及的计算。我们验证了我们模拟系统的方法,并分析了我们参数化相对于替代品的优势。