Optimization problem of the RFQ accelerator structure is considered as the problem
of the optimal control of an ensemble of dynamical systems described by a phase space
distribution density. A functional depending on the final density is considered as the cost
functional, and the acceleration efficiency and the synchronous phase are considered as
the controls. For numerical solution of the problem, it is proposed to use a method based
on representation for the second variation of the cost functional as an integral expression
containing the Green function for variation of trajectories of the dynamical systems and
a tensor of the third rank.