Measure differential inclusions

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

Abstract

When modeling dynamical systems with uncertainty, one usually resorts to stochastic calculus and, specifically, Brownian motion. Recently, we proposed an alternative approach based on time-evolution of measures, called Measure Differential Equations, which can be seen as natural generalization of Ordinary Differential Equations to measures. The approach allows to pass to the limit in discrete approximations and attain finite-speed diffusion, concentration and other phenomena. In this paper we start building the theory of Measure Differential Inclusions which are the counterpart of Differential Inclusions for measures. We provide the general definitions and prove existence of solutions under continuity and convexity properties.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1323-1328
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Differential Inclusions
Stochastic Calculus
Discrete Approximation
Brownian motion
Convexity
Existence of Solutions
Ordinary differential equation
Dynamical system
Differential equation
Uncertainty
Alternatives
Modeling

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Control and Systems Engineering
  • Modeling and Simulation

Cite this

Piccoli, B. (2019). Measure differential inclusions. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 1323-1328). [8618884] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618884
Piccoli, Benedetto. / Measure differential inclusions. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1323-1328 (Proceedings of the IEEE Conference on Decision and Control).
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Piccoli, B 2019, Measure differential inclusions. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618884, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 1323-1328, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8618884

Measure differential inclusions. / Piccoli, Benedetto.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1323-1328 8618884 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

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Piccoli B. Measure differential inclusions. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1323-1328. 8618884. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8618884