Deep Identification of Nonlinear Systems in Koopman Form
This method addresses the challenge of system identification for nonlinear dynamics, particularly in cases with full or partial state availability, though it appears incremental as it builds on existing Koopman operator frameworks.
The paper tackles the identification of nonlinear dynamical systems by using Koopman-based deep state-space encoders to avoid the need for pre-selecting lifting functions, achieving excellent long-term prediction capabilities as demonstrated on benchmark examples.
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.