Determine unknown causes from their known effects given by a set of measurements. It involves parameter identification in a dynamical system. Applications include seismology, fluid dynamics, medicine, astronomy, etc. The main questions are well-posedness (existence, uniqueness and stability) and numerical reconstruction.

Study how to drive dynamical systems to desired targets using controllers to adjust system inputs. Common applications include control in cars, airplane autopilot, fluid dynamics, medicine: diabetes control, radiotherapy, etc. The theory is strongly related to inverse problems.