Control of simulation of a particle accelerator as a spatially distributed system

The work deals with the construction of strategy for finding optimal control of systems for spatially distributed systems on an example of problems in physics beams. The suggested approach is based on use of exact and approximate invariants as a controlling mechanism for control of modelling process of beam lines. The classical problem of optimal control of similar systems as an optimal control problem is formulated in a functional space. This approach is based on algebraic methods Lie and the corresponding matrix formalism that allows you to build not only the formal procedures for finding optimal solutions, but also provide the necessary constructive computational procedures.