“Averaged controllability in a long time horizon” by Martin Lazar

We extend the recently introduced notion of averaged controllability for parameter dependent, finite dimensional systems. We assume a finite number of possible parameter realisations and that each realisation can appear with a known probability. The goal is to design a control independent of the parameter that steers the averaged of the system to some prescribed value in time T>0 but also keeps the averaged at this prescribed value for all times t>T. This new notion we address as long-time averaged controllability. We give a necessary and sufficient condition for this property to hold and address the L 2 norm optimality of the longtime averaged controls. Relations between different control notions of parameter-dependent systems are discussed, accompanied by numerical examples. This is a joint work with Jérôme Lohéac, University of Lorraine.