  A general achievable upper bound of extractable work under feedback control
is given, where nonequilibrium equalities are generalized so as to be
applicable to error-free measurements. The upper bound involves a term which
arises from the part of the process whose information becomes unavailable and
is related to the weight of the singular part of the reference probability
measure. The obtained upper bound of extractable work is more stringent than
the hitherto known one and sets a general achievable bound for a given feedback
protocol. Guiding principles of designing the optimal protocol are also
outlined. Examples are presented to illustrate our general results.
