Deep KKL: Data-driven Output Prediction for Non-Linear Systems
This work addresses output prediction for nonlinear systems, bridging control theory and machine learning, but appears incremental in its approach.
The paper tackles the problem of output prediction for autonomous nonlinear systems by proposing a predictor based on the Kazantzis-Kravaris/Luenberger observer, using a small set of measured trajectories. The experiments show that the solution yields an efficient predictor over a subset of the observation space.
We address the problem of output prediction, ie. designing a model for autonomous nonlinear systems capable of forecasting their future observations. We first define a general framework bringing together the necessary properties for the development of such an output predictor. In particular, we look at this problem from two different viewpoints, control theory and data-driven techniques (machine learning), and try to formulate it in a consistent way, reducing the gap between the two fields. Building on this formulation and problem definition, we propose a predictor structure based on the Kazantzis-Kravaris/Luenberger (KKL) observer and we show that KKL fits well into our general framework. Finally, we propose a constructive solution for this predictor that solely relies on a small set of trajectories measured from the system. Our experiments show that our solution allows to obtain an efficient predictor over a subset of the observation space.