In this article, we discuss the local exact controllability to trajectories of the convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) in a bounded domain \(\Omega \) with control supported in a subdomain \(\omega \subset \Omega \subset \mathbb {R}^d\) , \(d \in \{2,3\}\) with smooth boundary. We first present global Carleman estimates and observability inequality for the adjoint problem of a linearized version of CBF equations by using a global Carleman estimate for the Stokes system. This allows us to obtain its null controllability at any time \(T>0\) . We then use the inverse mapping theorem to deduce local results concerning the exact controllability to the trajectories of CBF equations.
