Randomized approximations of the image set of nonlinear mappings with applications to filtering

Fabrizio Dabbene, Didier Henrion, Constantino Lagoa, Pavel Shcherbakov

Research output: Contribution to journalConference articlepeer-review

7 Scopus citations

Abstract

The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithms for approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a nonlinear function. We introduce minimum-volume approximations which have the characteristic of guaranteeing a low probability of violation, i.e., we admit for a probability that some points in the image set are not contained in the approximating set, but this probability is kept below a pre-specified threshold ε. In the second part of the paper, this idea is then exploited to develop a new family of randomized prediction-corrector filters. These filters represent a natural extension and rapprochement of Gaussian and set-valued filters, and bear similarities with modern tools such as particle filters.

Original languageEnglish (US)
Pages (from-to)37-42
Number of pages6
JournalIFAC-PapersOnLine
Volume28
Issue number14
DOIs
StatePublished - Jul 1 2015
Event8th IFAC Symposium on Robust Control Design, ROCOND 2015 - Bratislava, Slovakia
Duration: Jul 8 2015Jul 11 2015

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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