  In the present work we investigate an optimal control problem related to the
following chemotaxis-consumption model in a bounded domain $\Omega\subset
\mathbb{R}^3$:
  $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t v -
\Delta v = - u^s v + f \,v\, 1_{\Omega_c},$$
  with $s \geq 1$, endowed with isolated boundary conditions and initial
conditions for $(u,v)$, being $u$ the cell density, $v$ the chemical
concentration and $f$ the control acting in the $v$-equation through the
bilinear term $f \,v\, 1_{\Omega_c}$, in a subdomain $\Omega_c \subset \Omega$.
We address the existence of optimal control restricted to a weak solution
setting, where, in particular, uniqueness of state $(u,v)$ given a control $f$
is not clear. Then by considering weak solutions satisfying an adequate energy
inequality, we prove the existence of optimal control subject to uniformly
bounded controls. Finally, we discuss the relation between the considered
control problem and two other related ones, where the existence of optimal
solution can not be proved.
