  We consider a current-biased dc SQUID in the presence of an applied
time-dependent bias current or magnetic flux. The phase dynamics of such a
Josephson device is equivalent to that of a quantum particle trapped in a $1-$D
anharmonic potential, subject to external time-dependent control fields, {\it
i.e.} a driven multilevel quantum system. The problem of finding the required
time-dependent control field that will steer the system from a given initial
state to a desired final state at a specified final time is formulated in the
framework of optimal control theory. Using the spectral filter technique, we
show that the selected optimal field which induces a coherent population
transfer between quantum states is represented by a carrier signal having a
constant frequency but which is time-varied both in amplitude and phase. The
sensitivity of the optimal solution to parameter perturbations is also
addressed.
