Nonautonomous Evolution Inclusions Governed by State-Dependent Sweeping Processes: Well-Posedness and Approximate Controllability

We study approximate controllability for a state-dependent sweeping process in a Hilbert space by coupling it with a nonautonomous evolution inclusion. The control acts on the evolution inclusion and induces an indirect feedback mechanism for the sweeping dynamics. We first establish well-posedness of the coupled system by combining a fixed point argument with tools from nonsmooth and nonconvex analysis. We then use resolvent-operator techniques to derive sufficient conditions for approximate controllability. Finally, we apply the abstract results to a thermally coupled frictionless contact problem with an external heat source.