Geodesic
Solution of one control problem for a dynamical system in partial derivatives
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 97-108

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For a second-order dynamic system in partial derivatives with three boundary conditions, the problem of constructing control and state functions in analytical form is solved by the cascade decomposition method. Two criteria of complete controllability are obtained. The first criterion is based on the surjectivity property of a certain matrix. The second criterion is identical to the Kalman criterion. A class of functions is identified that determine the analytical form of control and state functions. A method for constructing control and state functions in analytical form is developed.
Keywords: dynamic system with partial derivatives, complete controllability, program control, cascade decomposition method 
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     author = {E. V. Raetskaya},
     title = {Solution of one control problem for a dynamical system in partial derivatives},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {235},
     year = {2024},
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}
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E. V. Raetskaya. Solution of one control problem for a dynamical system in partial derivatives. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 97-108. http://geodesic.mathdoc.fr/item/INTO_2024_235_a8/