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Higher order Moreau's sweeping process: Mathematical formulation and numerical simulation

Vincent Acary 1 Bernard Brogliato 1 Daniel Goeleven 2 
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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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Vincent Acary, Bernard Brogliato, Daniel Goeleven. Higher order Moreau's sweeping process: Mathematical formulation and numerical simulation. Mathematical Programming, 2008, 113 (1), pp.133-217. ⟨10.1007/s10107-006-0041-0⟩. ⟨inria-00423566⟩



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