  Here, we investigate the uncertainty of dynamical observables in classical
systems manipulated by repeated measurements and feedback control; the
precision should be enhanced in the presence of an external controller but
limited by the amount of information obtained from the measurements. We prove
that the entropy production and the information quantity constrain from below
the fluctuation of arbitrary observables that are antisymmetric under time
reversal. The information term is the sum of the mutual entropy production and
the Kullback--Leibler divergence, which characterises the irreversibility of
the measurement outcomes. The result holds for finite observation times and for
both continuous- and discrete-time systems. We apply the derived relation to
study the precision of a flashing Brownian ratchet.
