Abstract : This proposal belongs to the area of optimal control for sweeping processes and their applications to optimization-related and control problems, as well as some practical models. By now, the sweeping process has been recognized as a class of nonsmooth dynamical systems involving normal cones to moving sets. The controlled sweeping processes have been studied with applications relating to the theory of plasticity, ferromagnetism, ferroelectricity, and elastoplasticity. Further developments also apply to various problems of hysteresis, phase transitions, modelling systems with contact, friction, and impacts. These systems frequently arise in applications such as mechanical systems, switched electrical circuits, and biological systems.
