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Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

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Abstract

In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a time-stepping algorithm is also presented. This differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary-slackness variables. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes.

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Authors and Affiliations

  1. INRIA Rhône-Alpes, Bipop project, ZIRST Montbonnot, 655 avenue de l’Europe, 38334, Saint Ismier cedex, France

    Vincent Acary & Bernard Brogliato

  2. IREMIA, Université de La Réunion, 97715, Saint-Denis, France

    Daniel Goeleven

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  1. Vincent Acary
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  2. Bernard Brogliato
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  3. Daniel Goeleven
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Correspondence to Bernard Brogliato.

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Acary, V., Brogliato, B. & Goeleven, D. Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation. Math. Program. 113, 133–217 (2008). https://doi.org/10.1007/s10107-006-0041-0

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