The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is circumvented. The encoder represents the lifting function to the space where the dynamics are linearly propagated using the Koopman operator. An input-affine formulation is considered for the lifted model structure and we address both full and partial state availability. The approach is implemented using the the deepSI toolbox in Python. To lower the computational need of the simulation error-based training, the data is split into subsections where multi-step prediction errors are calculated independently. This formulation allows for efficient batch optimization of the network parameters and, at the same time, excellent long term prediction capabilities of the obtained models. The performance of the approach is illustrated by nonlinear benchmark examples.
翻译:本文件用基于Koopman的深层状态-空间编码器处理非线性动态系统的识别问题。 通过这种方法,通常会绕过需要选择先验式升降功能字典的缺点。 编码器代表着向使用Koopman操作员线性传播动态的空间的升动功能。 用于已取消的模型结构的输入- faffine 配方被考虑, 我们同时处理完全和部分状态的可用性。 这种方法是使用位于Python的深层SI工具箱实施的。 为了降低模拟错误培训的计算需求,数据被分为几个小节, 在那里独立地计算多步预测错误。 这种配方可以对网络参数进行高效的批次优化,同时对所获得的模型进行出色的长期预测能力。 非线性基准示例说明了该方法的绩效。