The paper is devoted to intense quasiperiodic beam dynamics investigation on the basis of integro-differential mathematical model. Space charge density representation by trigonometric polynomial makes it possible to obtain Coulomb field analytical expression in the same form. Space charge field is presented by the integral over particle phase states domain. Beam quality criteria are suggested in the form of integral functionals. Beam dynamics optimization problem is formalized as trajectory ensemble control problem. Analytical expression of objective functional variation is obtained; it makes possible directed optimization methods using. Numerical simulation and optimization results are presented for linear waveguide accelerator.