Journal of Convex Analysis 17 (2010), No. 3&4, 961--990
Copyright Heldermann Verlag 2010
Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems
Bernard Brogliato
INRIA - ZIRST Montbonnot, 655 Avenue de l'Europe, 38334 Saint Ismier, France
bernard.brogliato@inrialpes.fr
Lionel Thibault
Université Montpellier II, Dép. de Mathématiques, Case courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
thibault@math.univ-montp2.fr
This paper deals with the well-posedness of a class of complementarity dynamical systems. Both the linear and the nonlinear cases are treated, and the systems are non-autonomous. A specific "input-output" property is used to perform a change of state vector which allows one to transform the complementarity dynamics into a perturbed Moreau's sweeping process. Then the results obtained by J. F. Edmond and L. Thibault ["Relaxation of an optimal control problem involving a perturbed sweeping process", Mathematical Programming 104 (2005) 347--373; and "BV solutions of nonconvex sweeping process differential inclusions with perturbation", Journal of Differential Equations 226 (2006) 135--179] and L. Thibault ["Sweeping process with regular and nonregular sets", Journal of Differential Equations, 193 (2003) 1--26] on the well-posedness of the sweeping process are used. Absolutely continuous as well as bounded variation solutions (with state jumps) are examined in this work.
Keywords: Moreau's sweeping process, complementarity system, differential inclusion, existence, uniqueness, prox-regular set, state jumps, bounded variation.
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