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Relaxation of Euler-Type Discrete-Time Control System

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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Abstract

This paper investigates what is the Hausdorff distance between the set of Euler curves of a Lipschitz continuous differential inclusion and the set of Euler curves for the corresponding convexified differential inclusion. It is known that this distance can be estimated by \(O(\sqrt{h})\), where h is the Euler discretization step. It has been conjectured that, in fact, an estimation O(h) holds. The paper presents results in favor of the conjecture, which cover most of the practically relevant cases. However, the conjecture remains unproven, in general.

This research is supported by the Austrian Science Foundation (FWF) under grant P 26640-N25.

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Notes

  1. 1.

    In fact, the global boundedness and Lipschitz continuity can be replaced with local ones if all solutions of (1) are contained in a bounded set. Then the formulations of some of the claims in the paper should be somewhat modified. The standing assumptions above are made simpler for more transparency.

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Author information

Authors and Affiliations

  1. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria

    Vladimir M. Veliov

Authors
  1. Vladimir M. Veliov
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Correspondence to Vladimir M. Veliov .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Veliov, V.M. (2015). Relaxation of Euler-Type Discrete-Time Control System. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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