Method for particle ensembles control under uncertainty

The paper is devoted to the issues related to nonlinear dynamics of controlled intensive charged particle beams. Study the beams possessing exceptionally large inherent fields and extreme high impulse intensity and energy calls for new cybernetic approaches aimed to developing controlling algorithm of optimal behavior. We describe the beam distribution in particle accelerations (a Vlasov-Maxwell scheme) in the framework of differential games and control problem. This paper proposes an optimal approach for the well-known partial differential equation of Vlasov involving semi-group contraction and dissipative operators in Hilbert space