A heuristic algorithm for one nonlinear optimal control problem

The optimal control problem for one of the variants of a quasilinear system is considered. To solve it, the idea of Professor V.I. Gurman is used, who proposed to combine two variants of the expansion principle. One of them is the traditional Krotov approach, and the second is the penalty function method. The selected class of systems allows for an analytical study of the Krotov Lagrangian, which in turn leads to the formulation of the algorithm. The resulting algorithm is tested on two illustrative examples, for which minimizing sequences are constructed. The complexity of the calculations is comparable with methods based on the traditional expansion principle. The calculation results are illustrated by tables and graphs.