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A scenario approach to non-convex control design: preliminary probabilistic guarantees


S. Grammatico, X. Zhang, K. Margellos, P.J. Goulart, J. Lygeros

American Control Conference, Portland, Oregon, USA, pp. 3431-3436

Randomized optimization is a recently established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable for a certain class of non-convex problems, but they usually are conservative in terms of performance and computationally demanding. In this paper, we derive a novel scenario approach for a wide class of random non-convex programs. We provide a sample complexity similar to the one for uncertain convex programs, but valid for all feasible solutions inside a set of a-priori chosen complexity. Our scenario approach applies to many non-convex control-design problems, for instance control synthesis based on uncertain bilinear matrix inequalities.


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% Autogenerated BibTeX entry
@InProceedings { GraEtal:2014:IFA_4589,
    author={S. Grammatico and X. Zhang and K. Margellos and P.J. Goulart and J.
    title={{A scenario approach to non-convex control design:
	  preliminary probabilistic guarantees}},
    booktitle={American Control Conference},
    address={Portland, Oregon, USA},
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