  As a variant of the original quantum teleportation, the port-based
teleportation has been proposed, and its various kinds of useful applications
in quantum information processing have been explored. Two users in the
port-based teleportation initially share an arbitrary pure state, which can be
represented by applying one user's local operation to a bipartite maximally
entangled state. If the maximally entangled state is a $2M$-qudit state, then
it can be expressed as $M$ copies of a two-qudit maximally entangled state,
where $M$ is the number of the ports. We here consider a generalization of the
original port-based teleportation obtained from employing copies of an
arbitrary bipartite (mixed) resource instead of copies of a pure maximally
entangled one. By means of the generalization, we construct a concept of the
controlled port-based teleportation by combining the controlled teleportation
with the port-based teleportation, and analyze its performance in terms of
several meaningful quantities such as the teleportation fidelity, the
entanglement fidelity, and the fully entangled fraction. In addition, we
present new quantities called the control power and the minimal control power
for the new controlled version on a given tripartite quantum state.
