In this report we develop our approach to acceleration and focusing by use theory of optimal control. Several scenarios have been discussed earlier [see Z. Parsa and V. Zadorozhny, proceedings PAC-03, EPAC-02]. The ones given here a more recent and more detailed, the L-problem moment used in a simulation of acceleration and focusing of longitudinal motion. Optimal and cost - effective acceleration complexes are search and described. Separate acceleration scenarios are given here for new acceleration concept.