Higher Order Moreau's Sweeping Process: Formulation and numerical simulation

Vincent Acary 1, * Bernard Brogliato 1, *
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In this chapter we present a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables. The proposed model incorporates the state jumps via high-order distributions through the extension of Moreau's sweeping process, which is a special type of differential inclusion. The time-discretization of these nonsmooth systems, which is non-trivial, is also presented. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes, where it may be helpful for a better understanding of the closed-loop dynamics induced by some feedback laws.
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Vincent Acary, Bernard Brogliato. Higher Order Moreau's Sweeping Process: Formulation and numerical simulation. Alart, P. and Maisonneuve, O. and Rockafellar, R. T. Nonsmooth Mechanics and Analysis, 12, Springer Verlag, pp.261-277, 2007, Advances in Mechanics and Mathematics, ⟨10.1007/0-387-29195-4_22⟩. ⟨hal-00758609⟩

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