Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering∗. Issue 14 (2015)

• Record Type: Journal Article
• Authors: Dabbene, Fabrizio; Henrion, Didier; Lagoa, Constantino; Shcherbakov, Pavel
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 14(2015)
• Page Start: 37
• Page End: 42
• Publication Date: 2015
• Subjects: Randomized algorithms -- filtering -- nonlinear systems -- semialgebraic sets; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.430
• Languages: English
• ISSNs: 2405-8963

Abstract

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 e. 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.