Geodesic
An approach to calculating degenerate extremal controls based on fixed point problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 118-132

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In the class of optimal control problems linear with respect to the control, an approach to calculating degenerate controls that satisfy the maximum principle, is proposed. This approach is based on new optimality conditions in the form of fixed point problems that are equivalent to the well-known conditions of the maximum principle. New forms of conditions for the maximum principle make it possible to construct effective methods for searching for degenerate controls. The efficiency of the approach proposed is illustrated using model examples.
Keywords: linearly controlled system, maximum principle, fixed point problem, degenerate controls, iterative methods 
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     author = {A. S. Buldaev and I. D. Kazmin},
     title = {An approach to calculating degenerate extremal controls based on fixed point problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {118--132},
     publisher = {mathdoc},
     volume = {234},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2024_234_a14/}
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A. S. Buldaev; I. D. Kazmin. An approach to calculating degenerate extremal controls based on fixed point problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 118-132. http://geodesic.mathdoc.fr/item/INTO_2024_234_a14/