Learning Stable Stochastic Nonlinear Dynamical Systems

Jonas Umlauft, Sandra Hirche
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3502-3510, 2017.

Abstract

A data-driven identification of dynamical systems requiring only minimal prior knowledge is promising whenever no analytically derived model structure is available, e.g., from first principles in physics. However, meta-knowledge on the system’s behavior is often given and should be exploited: Stability as fundamental property is essential when the model is used for controller design or movement generation. Therefore, this paper proposes a framework for learning stable stochastic systems from data. We focus on identifying a state-dependent coefficient form of the nonlinear stochastic model which is globally asymptotically stable according to probabilistic Lyapunov methods. We compare our approach to other state of the art methods on real-world datasets in terms of flexibility and stability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-umlauft17a, title = {Learning Stable Stochastic Nonlinear Dynamical Systems}, author = {Jonas Umlauft and Sandra Hirche}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3502--3510}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/umlauft17a/umlauft17a.pdf}, url = {https://proceedings.mlr.press/v70/umlauft17a.html}, abstract = {A data-driven identification of dynamical systems requiring only minimal prior knowledge is promising whenever no analytically derived model structure is available, e.g., from first principles in physics. However, meta-knowledge on the system’s behavior is often given and should be exploited: Stability as fundamental property is essential when the model is used for controller design or movement generation. Therefore, this paper proposes a framework for learning stable stochastic systems from data. We focus on identifying a state-dependent coefficient form of the nonlinear stochastic model which is globally asymptotically stable according to probabilistic Lyapunov methods. We compare our approach to other state of the art methods on real-world datasets in terms of flexibility and stability.} }
Endnote
%0 Conference Paper %T Learning Stable Stochastic Nonlinear Dynamical Systems %A Jonas Umlauft %A Sandra Hirche %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-umlauft17a %I PMLR %P 3502--3510 %U https://proceedings.mlr.press/v70/umlauft17a.html %V 70 %X A data-driven identification of dynamical systems requiring only minimal prior knowledge is promising whenever no analytically derived model structure is available, e.g., from first principles in physics. However, meta-knowledge on the system’s behavior is often given and should be exploited: Stability as fundamental property is essential when the model is used for controller design or movement generation. Therefore, this paper proposes a framework for learning stable stochastic systems from data. We focus on identifying a state-dependent coefficient form of the nonlinear stochastic model which is globally asymptotically stable according to probabilistic Lyapunov methods. We compare our approach to other state of the art methods on real-world datasets in terms of flexibility and stability.
APA
Umlauft, J. & Hirche, S.. (2017). Learning Stable Stochastic Nonlinear Dynamical Systems. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3502-3510 Available from https://proceedings.mlr.press/v70/umlauft17a.html.

Related Material