398 research outputs found
On the equivalence between complementarity systems, projected systems and differential inclusions
International audienceIn this note, we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of differential inclusions, and a class of complementarity dynamical systems. Each of these dynamical systems can also be considered as a hybrid dynamical system. This work both generalizes previous results and sheds some new light on the relationship between known formalisms; besides, it exclusively uses tools from convex analysis
On the Equivalence Between Complementarity Systems, Projected Systems and Unilateral Differential Inclusions
An updated version of this paper has appeared in Systems & Control Letters, 55, (2006), pp 45-51, DOI 10.1016/j.sysconle.2005.04.015In this note we prove the equivalence, under appropriate conditions, between several dynamical formalisms: projected dynamical systems, two types of unilateral differential inclusions, and a class of complementarity dynamical systems. Each of these dynamical systems can also be considered as a hybrid dynamical system. This work is of interest since it both generalises some previous results and sheds new light on the relationship between known formalisms
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
- …