Chance-constrained quasi-convex optimization with application to data-driven switched systems control
(2021) The Third Annual Conference on Learning for Dynamics and Control — Location: Virtual (7.June.2021)
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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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Citations
Berger, G., Jungers, R., & Wang, Z. (2021). Chance-constrained quasi-convex optimization with application to data-driven switched systems control. Published. The Third Annual Conference on Learning for Dynamics and Control, Virtual.