Chance-Constrained Quasi-Convex Optimization with Application to Data-Driven Switched Systems Control
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
Text
Berger et al. "Chance-Constrained Quasi-Convex Optimization with Application to Data-Driven Switched Systems Control." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.Markdown
[Berger et al. "Chance-Constrained Quasi-Convex Optimization with Application to Data-Driven Switched Systems Control." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.](https://mlanthology.org/l4dc/2021/berger2021l4dc-chanceconstrained/)BibTeX
@inproceedings{berger2021l4dc-chanceconstrained,
title = {{Chance-Constrained Quasi-Convex Optimization with Application to Data-Driven Switched Systems Control}},
author = {Berger, Guillaume O. and Jungers, Raphaël M. and Wang, Zheming},
booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control},
year = {2021},
pages = {571-583},
volume = {144},
url = {https://mlanthology.org/l4dc/2021/berger2021l4dc-chanceconstrained/}
}