期刊
SYSTEMS & CONTROL LETTERS
卷 134, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.sysconle.2019.104560
关键词
Probability; Semi-algebraic sets; Sum of squares; Scenario theory
This paper proposes a means to characterize multivariate data. This characterization, given in terms of both probability distributions and data-enclosing sets, is instrumental in assessing and improving the robustness properties of system designs. To this end, we propose the Sliced-Normal (SN) class of distributions. The versatility of SNs enables characterizing complex parameter dependencies with minimal modeling effort. A polynomial mapping which injects the physical space into a higher dimensional (so-called) feature space is first defined. Optimization-based strategies for the estimation of SNs from data in both physical and feature space are proposed. The non-convex formulations in physical space yield SNs having the best performance. However, the formulations in feature space either admit an analytical solution or yield a convex program thereby facilitating their application to high-dimensional datasets. The semi-algebraic form of the superlevel sets of a SN, form which a tight data-enclosing set can be readily identified, makes them amenable to rigorous worst-case based approaches to robustness analysis and robust design. Furthermore, we propose a chance-constrained optimization framework for identifying and eliminating the effects of outliers in the prescription of such a set. In addition, the distribution-free and non-asymptotic Scenario Theory framework is used to rigorously bound the probability of unseen data falling outside the identified data-enclosing set. Published by Elsevier B.V.
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