Meta-Learning of Neural State-Space Models Using Data From Similar Systems

Data-driven system identification is often a necessary step for model-based design of control systems. While many data-driven modeling frameworks have been demonstrated to be effective, the class of models that contain a state-space description at their core have typically been easiest to integrate with model-based control and estimation algorithms, e.g., model predictive control or Kalman filtering. Early implementations of neural state-space models (SSMs) employed shallow recurrent layers and were dependent on linearization to obtain linear representations [1] or linear-parameter-varying system representations [2]. Recent advancements in deep neural networks have enabled embedding SSMs into the neural architecture explicitly without post-hoc operations [3], and therefore the SSM description can be learned directly during training; see [4] for a recent survey. For instance, unmodeled dynamics remaining after procuring a physics-informed prior model can be represented using neural SSMs [5, 6], and additional control-oriented structure can be embedded during training [7]. Another interesting direction of research has led to the development of autoencoder-based SSMs, where the neural architecture comprises an encoder that transforms the ambient state-space to a (usually high-dimensional) latent space, a decoder that inverse-transforms a latent state to the corresponding ambient state, and a linear SSM in the latent space that satisfactorily approximates the system's underlying dynamics [8-10]. Even without the decoder, deep encoder networks have proven useful for neural state-space modeling [11]. An argument for the effectiveness of autoencoder-based approaches is based on Koopman operator theory [12], which posits that a nonlinear system (under some mild assumptions) can be lifted to an infinite-dimensional latent space where the state-transition is linear; an autoencoder allows a finite-dimensional, therefore tractable, approximation of the Koopman lifting/lowering transformations [13].