Learning Multiple Nonlinear Dynamical Systems with Side Information

Naoya Takeishi, Yoshinobu Kawahara

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We address the problem of learning multiple dynamical systems, which is a kind of multi-task learning (MTL). The existing methods of MTL do not apply to learning dynamical systems in general. In this work, we develop a regularization method to perform MTL for dynamical systems appropriately. The proposed method is based on an operator-theoretic metric on dynamics that is agnostic of model parametrization and applicable even for nonlinear dynamics models. We calculate the proposed MTL-like regularization by estimating the metric from trajectories generated during training. Learning time varying systems can be regarded as a special case of the usage of the proposed method. The proposed regularizer is versatile as we can straightforwardly incorporate it into off the-shelf gradient-based optimization methods. We show the results of experiments on synthetic and real-world datasets, which exhibits the validity of the proposed regularizer.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781728174471
Publication statusPublished - Dec 14 2020
Externally publishedYes
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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