Geodesic
The variational optimality condition in the problem of minimizing the finite state norm by a composite system of hyperbolic and ordinary differential equations
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 540-548

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An optimal control problem for a system of linear first-order hyperbolic equations is studied. The boundary conditions are determined from controlled systems of ordinary differential equations. A nonclassical exact formulae for the increment of a linear performance index (a finite state norm) is suggested. Based on this result, a variational optimality condition is proved. The original optimal control problems for a hyperbolic system is reduced to the problem for systems of ordinary differential equations.
Keywords: hyperbolic system, controlled boundary conditions, norm minimization, variational optimality condition, problem reduction. 
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     author = {A. V. Arguchintsev},
     title = {The variational optimality condition in the problem of minimizing the finite state norm by a composite system of hyperbolic and ordinary differential equations},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {540--548},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a9/}
}
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A. V. Arguchintsev. The variational optimality condition in the problem of minimizing the finite state norm by a composite system of hyperbolic and ordinary differential equations. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 540-548. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a9/