Subspace State-Space Identification and Model Predictive Control of Nonlinear Dynamical Systems Using Deep Neural Network with Bottleneck

Ichiro Maruta, Keito Yamada, Kenji Fujimoto

Keywords: System identification, Model predictive control, Subspace state-space system identification

Abstract: A novel nonlinear system identification method that produces state estimator and predictor directly usable for model predictive control (MPC) is proposed in this paper. The main feature of the proposed method is that it uses a neural network with a bottleneck layer between the state estimator and predictor to represent the input-output dynamics, and it is proven that the state of the dynamical system can be extracted from the bottleneck layer based on the observability of the target system. The training of the network is shown to be a natural nonlinear extension of the subspace state-space system identification method established for linear dynamical systems. This correspondence gives interpretability to the resulting model based on linear control theory. The usefulness of the proposed method and the interpretability of the model are demonstrated through an illustrative example of MPC.

One-sentence Summary: We propose a simple nonlinear extension of the subspace identification method and prove its fundamental properties.