  We develop the constrained adiabatic trajectory method (CATM) which allows
one to solve the time-dependent Schr\"odinger equation constraining the
dynamics to a single Floquet eigenstate, as if it were adiabatic. This
constrained Floquet state (CFS) is determined from the Hamiltonian modified by
an artificial time-dependent absorbing potential whose forms are derived
according to the initial conditions. The main advantage of this technique for
practical implementation is that the CFS is easy to determine even for large
systems since its corresponding eigenvalue is well isolated from the others
through its imaginary part. The properties and limitations of the CATM are
explored through simple examples.
