In this movie, we represent the evolution of the control of the one dimensional wave equation (on (0,1)) where the control is localised at $x=1$. The parameter that evolves is the final $Tin(4,8)$. The initial data is given by $(y_0,y_1)=(mathbb{1}_{0.25,0.75},0)$.
For each final time $T$, the control is the HUM control computed by a descent algorithm.
In the upper box, we represent the evolution of the classical HUM control with respect to the final time. In the lower box we use a regularised in time HUM method by applying a $mathcal{C}^1(0,T)$-weight in the functional to be minimised. This comparison is made in order to show the gain of regularity when using the weighted method.