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

Vincent Acary (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

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].

Domaines: Optimisation et contrôle [math.OC]

Vincent Acary. An overview of Non Smooth Dynamical Systems. Moreau's Sweeping Process, Higher order systems and links with optimization. Optimization and its applications., Jan 2005, Oberwolfach, Germany. ⟨inria-00423541⟩