A SYSTEMATIC METHOD FOR BUILDING SMOOTH CONTROLS FOR SMOOTH DATA - Ervedoza, Sylvain; Zuazua, Enrique (Discrete and Continuous Dynamical Systems-Series B, 2010)
We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z(0) in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability assumptions on the adjoint system, when A generates a C(0) group, we develop a method to compute algorithmically a control function v that inherits the regularity of the initial datum to be controlled. In particular, the controlled equation is satisfied in a strong sense when the initial datum is smooth. In this way, the controlled trajectory is smooth as well. Our method applies mainly to time-reversible infinite-dimensional systems and, in particular, to the wave equation, but fails to be valid in the parabolic frame.
CRIS-Team WoS Importer:2019-12-13