Optimization of dynamics of trajectory bundles using smooth and nonsmooth functionals. Part 1

Many different works are devoted to the problems of control and optimization in dynamic systems. Interest in these tasks does not decrease with time. New challenges arise in the development of technological processes in various fields of science and technology, in particular, in the design and creation of modern electrophysical equipment. In this paper, the problem of optimization and control of trajectory beams is considered. The problem of joint optimization of the program motion and the beam of perturbed motions using a combination of smooth and nonsmooth functionals is investigated. The first part deals with the mathematical formulation of the given representation of the variation of investigated functional and provides optimality conditions in the form of a maximum principle. In the second part, the problem of optimization of dynamics of charged particles in the accelerator with spatially homogeneous quadrupole focusing will be considered. Using a combination of smooth and non-smooth functions allows you to set the functionals that most accurately reflect the requirements for the dynamics of the charged particle beam in accelerators.