Subspace State-Space Identification of Nonlinear Dynamical System Using Deep Neural Network with a Bottleneck

This paper proposes a new type of subspace state-space system identification method for nonlinear dynamical systems, which generates a model consisting of a state estimator and a predictor that can be directly used for model predictive control (MPC). 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 provides interpretability and optimality 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. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (<THESTERM>https://creativecommons.org/licenses/by-ne-nd/4.0/</THESTERM>)