Deep KKL: Data-driven Output Prediction for Non-Linear Systems

TL;DR

This paper introduces a data-driven output prediction framework for nonlinear systems, combining control theory and machine learning, and proposes an efficient predictor based on a small set of measured trajectories.

Contribution

It formulates a unified framework for nonlinear output prediction, integrating control and data-driven methods, and develops a predictor based on the Kazantzis-Kravaris/Luenberger observer using limited data.

Findings

Efficient predictor achieved over a subset of the observation space

Framework successfully integrates control theory and machine learning

Constructive solution relies on a small set of measured trajectories

Abstract

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.