  We discuss the Giardin\`a-Kurchan-Peliti population dynamics method for
evaluating large deviations of time averaged quantities in Markov processes
[Phys. Rev. Lett. \textbf{96}, 120603 (2006)]. This method exhibits systematic
errors which can be large in some circumstances, particularly for systems with
weak noise, with many degrees of freedom, or close to dynamical phase
transitions. We show how these errors can be mitigated by introducing control
forces within the algorithm. These forces are determined by an
iteration-and-feedback scheme, inspired by multicanonical methods in
equilibrium sampling. We demonstrate substantially improved results in a simple
model and we discuss potential applications to more complex systems.
