  The article deals with the subject of solving the problem of canonical-map
synthesis for Hamiltonian systems. For this purpose, the controlling-function
method has been developed that allows appropriate changes of the variables in
terms of calculus of canonical variation, starting from their target
conditions. To use the canonical formalism, the initial dynamic system that
employs changing Lagrange multipliers is reduced to a Hamiltonian system in an
xpanded phase space, followed by the construction of controlling function. The
algorithm suggested for the canonization of controlled mappings has an
advantage over the known procedures, and first of all, redundancy in the
rocedure that chooses regulated coordinate transformations as a base for a
goal-seeking synthesis scheme.
