  We develop a method to describe the temporal evolution of an interacting
system of bosons, for which the field operator expansion is truncated after a
finite number $M$ of modes, in a rigorously controlled manner. Using
McLachlan's principle of least error, we find a self-consistent set of
equations for the many-body state. As a particular benefit, and in distinction
to previously proposed approaches, the presently introduced method facilitates
the dynamical increase of the number of orbitals during the temporal evolution,
due to the fact that we can rigorously monitor the error made by increasing the
truncation dimension $M$. The additional orbitals, determined by the condition
of least error of the truncated evolution relative to the exact one, are
obtained from an initial trial state by steepest $constrained$ descent.
