Diff. Geom, Math. Phys., PDE Seminar: Enrique Zuazua

In this talk we present some joint work in collaboration with C. Castro (UPM, Madrid), R. Lecaros (CMM- Chile) and F. Palacios (Stanford) on flow control. We address a classical optimal control problem of inverse design, aiming to identify the initial source leading to a desired final configuration. First, in the one-dimensional case, we explain why classical strategies, based on linearization methods, fail, because of the lack of regularity of solutions. We then introduce an alternating descent method that exploits the generalized gradients that take into account the sensitivity of the smooth arcs of the solutions but also of shock locations. We compare the performance of the method with classical purely discrete strategies through various numerical experiments. We also address the multi-dimensional case and point towards perspectives of future development.