Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Lionel Thibault

Université Montpellier II, Dép. de Mathématiques, Case courrier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France

thibault@math.univ-montp2.fr

Keywords

  • Moreau's sweeping process
  • complementarity system
  • differential inclusion
  • existence
  • uniqueness
  • prox-regular set
  • state jumps
  • bounded variation

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Suggested citation

B. Brogliato, L. Thibault. “Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems.” Journal of Convex Analysis 17 (2010), No. 3&4, 961–990. https://doi.org/10.68381/jca17060

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.