Modeling uncertainty with measure differential equations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently, a new type of evolution equations for measures, called Measure Differential Equations (briefly MDE), was introduced, based on the concept of Probability Vector Field. The latter is a map associating to a probability measure on a manifold a probability measure on the tangent bundle, whose projection on the base is the original measure. Such approach allows the modeling of finite-speed diffusion, thus provides a new approach to uncertainty for differential equations. After showing some explicit examples of modeling uncertainty with finite-speed diffusion, the theory of MDEs is extended to the time-varying case. This allows the application to control systems, including basic results on disturbance rejection.

Original languageEnglish (US)
Title of host publication2019 American Control Conference, ACC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3188-3193
Number of pages6
ISBN (Electronic)9781538679265
DOIs
StatePublished - Jul 2019
Event2019 American Control Conference, ACC 2019 - Philadelphia, United States
Duration: Jul 10 2019Jul 12 2019

Publication series

NameProceedings of the American Control Conference
Volume2019-July
ISSN (Print)0743-1619

Conference

Conference2019 American Control Conference, ACC 2019
CountryUnited States
CityPhiladelphia
Period7/10/197/12/19

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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  • Cite this

    Piccoli, B. (2019). Modeling uncertainty with measure differential equations. In 2019 American Control Conference, ACC 2019 (pp. 3188-3193). [8815286] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/acc.2019.8815286