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
@article{arxiv.2101.01415,
title = {Chance-constrained quasi-convex optimization with application to data-driven switched systems control},
author = {Guillaume O. Berger and Raphaël M. Jungers and Zheming Wang},
journal= {arXiv preprint arXiv:2101.01415},
year = {2021}
}