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
2 IREMIA - Institut de REcherche en Mathématiques et Informatique Appliquées

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.

Mots clés: Convex analysis; Measure differential inclusions; Variational inequalities; Complementarity systems; Numerical simulation; Zero dynamics; Relative degree; Schwartz distributions; Electrical circuits; Time-stepping algorithm; Dissipative systems

Domaines: Optimisation et contrôle [math.OC]

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⟩