In PDE-constrained optimization problems, the distributed control problem
$$ \begin{array}{ll} \displaystyle \min_{y,u} & J(y,u) = \frac{1}{2}\|y-y_d\|_{L^2(\Omega)}^2 + \frac{\alpha}{2}\|u\|_{L^2(\Omega)}^2 \\ \text{subject to} & \mathcal{D}y = u, \quad \text{on}\ \Omega, \\ & \phantom{\mathcal{D}}y = g, \quad \text{in}\ \partial\Omega, \end{array} $$
where $ y $ is the state, $ u $ the control, $ y_d $ the desired state, and $ \mathcal{D} $ is some differential operator, e.g. $ \mathcal{D} = \Delta $, is in literature often referred to as tracking type problems.
So my question is:
Where does this name come from? What is the origin of the name?
Edit: So I have found now in the book Numerical PDE-constrained optimization that the tracking-name appear to be linked to the cost functional $ J $. Here Juan de los Reyes writes that "Quadratic objective functionals like $ J(y,u) $ are known as tracking type costs." I note that his cost function only differs in the term $ \|u\|_{L^2(\Omega)}^2 $, where he has $ \|u\|_{L^2(\Gamma)}^2 $, where $ \Gamma = \partial\Omega $ the the boundary of the domain. This is due to his problem being formulated with a Neumann boundary condition.
This does not answer the question though.