Clustering-based Mode Reduction for Markov Jump Systems

Zhe Du, Necmiye Ozay, Laura Balzano
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:689-701, 2022.

Abstract

While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-du22a, title = {Clustering-based Mode Reduction for Markov Jump Systems}, author = {Du, Zhe and Ozay, Necmiye and Balzano, Laura}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {689--701}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/du22a/du22a.pdf}, url = {https://proceedings.mlr.press/v168/du22a.html}, abstract = {While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.} }
Endnote
%0 Conference Paper %T Clustering-based Mode Reduction for Markov Jump Systems %A Zhe Du %A Necmiye Ozay %A Laura Balzano %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-du22a %I PMLR %P 689--701 %U https://proceedings.mlr.press/v168/du22a.html %V 168 %X While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.
APA
Du, Z., Ozay, N. & Balzano, L.. (2022). Clustering-based Mode Reduction for Markov Jump Systems. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:689-701 Available from https://proceedings.mlr.press/v168/du22a.html.

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