Summary
This chapter deals with the sampled scenarios approach to robust convex programming and its applications to control analysis and synthesis. It has been shown in previous work [71] that by randomly sampling a sufficient number of constraints among the (possibly) infinite constraints of a robust convex program, one obtains a standard convex optimization problem whose solution is ‘approximately feasible,’ in a probabilistic sense, for the original robust convex program. This is a generalization property in the learning theoretic sense, since the satisfaction of a certain number of ‘training’ constraints entails the satisfaction of other ‘unseen’ constraints. In this contribution we provide a new efficient bound on the generalization rate of sampled convex programs, and discuss several applications of this paradigm to robust control analysis and design problems.
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© 2006 Springer-Verlag London Limited
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Calafiore, G., Campi, M.C. (2006). Sampled Convex Programs and Probabilistically Robust Design. In: Calafiore, G., Dabbene, F. (eds) Probabilistic and Randomized Methods for Design under Uncertainty. Springer, London. https://doi.org/10.1007/1-84628-095-8_5
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DOI: https://doi.org/10.1007/1-84628-095-8_5
Publisher Name: Springer, London
Print ISBN: 978-1-84628-094-8
Online ISBN: 978-1-84628-095-5
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