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Superposition Principle for Differential Inclusions

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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Abstract

We prove an extension of the Superposition Principle by Ambrosio-Gigli-Savaré in the context of a control problem. In particular, we link the solutions of a finite-dimensional control system, with dynamics given by a differential inclusion, to a solution of a continuity equation in the space of probability measures with admissible vector field. We prove also a compactness and an approximation result for admissible trajectories in the space of probability measures.

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Acknowledgments

The authors acknowledge the endowment fund of the Joseph and Loretta Lopez Chair and the support of the INdAM-GNAMPA Project 2016 Stochastic Partial Differential Equations and Stochastic Optimal Transport with Applications to Mathematical Finance.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rutgers University - Camden, 311 N. 5th Street, Camden, NJ, 08102, USA

    Giulia Cavagnari & Benedetto Piccoli

  2. Department of Computer Sciences, University of Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Antonio Marigonda

Authors
  1. Giulia Cavagnari
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  2. Antonio Marigonda
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  3. Benedetto Piccoli
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Corresponding author

Correspondence to Antonio Marigonda .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Cavagnari, G., Marigonda, A., Piccoli, B. (2018). Superposition Principle for Differential Inclusions. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_21

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_21

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  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

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