Geodesic
Improvement methods for problems of optimal control of multistage processes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 15-27

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In this paper, we propose first- and second-order methods of improvement for optimal control problems with non-fixed durations of stages based on the theory of V. F. Krotov. We obtain unimprovability conditions, which are closely related to the necessary and sufficient conditions for a weak local minimum.
Keywords: multistage process, dynamical system, non-fixed time, optimal control, iterative methods. 
@article{INTO_2021_196_a1,
     author = {V. A. Baturin and S. Cheremnykh},
     title = {Improvement methods for problems of optimal control of multistage processes},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {15--27},
     publisher = {mathdoc},
     volume = {196},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_196_a1/}
}
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V. A. Baturin; S. Cheremnykh. Improvement methods for problems of optimal control of multistage processes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 15-27. http://geodesic.mathdoc.fr/item/INTO_2021_196_a1/