Learning Nonlinear State-Space Models Using Deep Autoencoders

We introduce a new methodology for the identification of nonlinear state-space models using machine-learning techniques based on deep autoencoders for dimensionality reduction and neural networks. By learning a direct acyclic computational graph, our framework simultaneously identifies the nonlinear output and state-update maps, and optionally a neural state observer. After formulating the approach in detail and providing guidelines for tuning the related hyperparameters and reducing the model order, we show its capability of fitting a nonlinear model from an input/output dataset generated by a benchmark nonlinear system. Performance is assessed in terms of the ability of filtering and predicting output signals ahead, and of controlling the system via nonlinear model predictive control (MPC) based on the identified model.