An overview of Non Smooth Dynamical Systems. Moreau's Sweeping Process, Higher order systems and links with optimization

Abstract : The non smooth approach is based on the Moreau's Sweeping process and its variants. The key idea is to write a right approximation of measures on a finite in- terval, and this leads efficient and robust numerical schemes, called Time–stepping schemes. The first algorithm was the “Catching up algorithm”. In the framework of multi-body dynamics, the derived algorithm is the ”Non Smooth Contact Dy- namics” method[13, 14, 7] which is able to treat several thousands of 3D frictional contact conditions. The time step is no longer of events but only fixed by a a priori error criterion. Therefore, accumulations of events or a large number of events in finite time are handled without difficulties. Furthermore, the convergence analy- sis of this family of schemes leads to existence of solutions for rather complicate systems [8, 16].
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Communication dans un congrès
Lemaréchal, C. and Jarre, F. and Zowe, J. Optimization and its applications., Jan 2005, Oberwolfach, Germany. Oberwolfach reports. Springer Verlag, 2005
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Vincent Acary. An overview of Non Smooth Dynamical Systems. Moreau's Sweeping Process, Higher order systems and links with optimization. Lemaréchal, C. and Jarre, F. and Zowe, J. Optimization and its applications., Jan 2005, Oberwolfach, Germany. Oberwolfach reports. Springer Verlag, 2005. 〈inria-00423541〉

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