This paper considers the problem of simultaneous optimization of the program motion and a bundle of perturbed motions for a nonlinear controlled dynamic system. Such problems arise in the study of optimization of charged particle beam dynamics in accelerating and focusing structures. When solving the problem of stabilizing the program motion, we also encounter the significant dependence of the perturbed motions on the selected program motion and the need to take this into account. The sum of a pair of Bolza type functionals is considered. One is defined on the program motion, the other is defined on a bundle of trajectories. Necessary optimality conditions are given. Moreover, in the stationary case, the function that attains a maximum under optimal control is constant, just as under optimal control of an individual trajectory.