Modelling, simulation and control of nonsmooth dynamical systems - SICONOS
The purpose of the project is to develop algorithms and software for the simulation and feedback control of dynamical systems which are nonsmooth, and more specifically so-called complementarity dynamical systems. Nonsmoothness is usually introduced into the system either by some nonsmooth control action or by the presence of nonsmooth events at a macroscopic level (such as impacts or switchings). Nonsmooth models abound in many engineering systems such as sliding mode or hybrid control and rigid body mechanics such as rattle of automotive components and other mechanical freeplay, and switching circuits in power electronics.
The research will tackle two fundamental issues head on. Firstly, that smooth numerical methods fail on nonsmooth systems. Algorithms need to be developed that deal with hit crossings, impacts, complementarity problems, sliding and chatter in a robust and easily applicable way. Secondly, the qualitative understanding of the dynamics including the design of feedback and robust control algorithms requires specific methods and cannot be solved with simple adaptations of known techniques for smooth linear or nonlinear dynamical systems.