Projected dynamical systems in a complementarity formalism

W.P.M.H. Heemels (1) , J.M. Schumacher (2) , S. Weiland (3)

1 Department of Mechanical Engineering [Eindhoven]
2 Tilburg University [Tilburg]
3 TU/e - Eindhoven University of Technology [Eindhoven]

Projected dynamical systems have been introduced by Dupuis and Nagurney as dynamic extensions of variational inequalities. In the systems and control literature, complementarity systems have been studied as input/output dynamical systems whose inputs and outputs are connected through complementarity conditions. We show here that, under mild conditions, projected dynamical systems can be written as complementarity systems.

Mots clés: variational inequalities; complementarity; discontinuous dynamical systems; systems theory; optimization

Domaines: Mécanique des structures [physics.class-ph]

W.P.M.H. Heemels, J.M. Schumacher, S. Weiland. Projected dynamical systems in a complementarity formalism. Operations Research Letters, 2000, 27 (2), pp.83-91. ⟨10.1016/S0167-6377(00)00042-0⟩. ⟨hal-01660026⟩