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

• URL: http://arxiv.org/abs/2103.12443v1
• Date: Tue, 23 Mar 2021 10:48:07 GMT
• Title: Deep KKL: Data-driven Output Prediction for Non-Linear Systems
• Abstract summary: We first define a general framework bringing together the necessary properties for the development of such an output predictor. We propose a predictor structure based on the Kazantzis-Kravaris/Luenberger (KKL) observer and we show that KKL fits well into our general framework. Our experiments show that our solution allows to obtain an efficient predictor over a subset of the observation space.
• Score: 7.5456680887905145
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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