Chance-constrained quasi-convex optimization with application to data-driven switched systems control

Guillaume O. Berger, Raphaël M. Jungers, Zheming Wang
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:571-583, 2021.

Abstract

We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even though our results are partly applicable to general quasi-convex problems, in this work we introduce and study a particular subclass, which we call "quasi-linear problems". We provide optimality conditions for these problems. Thriving on this, we extend the approach of chance-constrained convex optimization to quasi-linear optimization problems. Finally, we show that this approach is useful for the stability analysis of black-box switched linear systems, from a finite set of sampled trajectories. It allows us to compute probabilistic upper bounds on the JSR of a large class of switched linear systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-berger21a, title = {Chance-constrained quasi-convex optimization with application to data-driven switched systems control}, author = {Berger, Guillaume O. and Jungers, Rapha\"el M. and Wang, Zheming}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {571--583}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/berger21a/berger21a.pdf}, url = {https://proceedings.mlr.press/v144/berger21a.html}, abstract = {We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even though our results are partly applicable to general quasi-convex problems, in this work we introduce and study a particular subclass, which we call "quasi-linear problems". We provide optimality conditions for these problems. Thriving on this, we extend the approach of chance-constrained convex optimization to quasi-linear optimization problems. Finally, we show that this approach is useful for the stability analysis of black-box switched linear systems, from a finite set of sampled trajectories. It allows us to compute probabilistic upper bounds on the JSR of a large class of switched linear systems.} }
Endnote
%0 Conference Paper %T Chance-constrained quasi-convex optimization with application to data-driven switched systems control %A Guillaume O. Berger %A Raphaël M. Jungers %A Zheming Wang %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-berger21a %I PMLR %P 571--583 %U https://proceedings.mlr.press/v144/berger21a.html %V 144 %X We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even though our results are partly applicable to general quasi-convex problems, in this work we introduce and study a particular subclass, which we call "quasi-linear problems". We provide optimality conditions for these problems. Thriving on this, we extend the approach of chance-constrained convex optimization to quasi-linear optimization problems. Finally, we show that this approach is useful for the stability analysis of black-box switched linear systems, from a finite set of sampled trajectories. It allows us to compute probabilistic upper bounds on the JSR of a large class of switched linear systems.
APA
Berger, G.O., Jungers, R.M. & Wang, Z.. (2021). Chance-constrained quasi-convex optimization with application to data-driven switched systems control. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:571-583 Available from https://proceedings.mlr.press/v144/berger21a.html.

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