The paper is devoted to quasiperiodic intense beam dynamics is accelerating system. Particle interaction accounting is conducted with the use of well-known cloud-in-cell method. This numerical method is formalized, and mathematical model of space charge field intensity is suggested. Coulomb field intensity is presented in the form of integral over the domain of particle phase states. This permits beam evolution to be described by integro-differential equations. Controlled process quality is characterized by integral functional values. Beam dynamics optimization problem is formulated as trajectory ensemble control problem for dynamic system. Analytical expression of quality functional variation is obtained. It makes possible directed methods using for beam dynamics optimization.