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arXiv · 2101.01415

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

Guillaume O. Berger·Raphaël M. Jungers·Zheming Wang
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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.

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Guillaume O. Berger, Raphaël M. Jungers, Zheming Wang. 2021-01-05. Chance-constrained quasi-convex optimization with application to data-driven switched systems control. https://arxiv.org/abs/2101.01415

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