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

    5 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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