Geodesic
The non-classical optimality condition in the hybrid control problem of hyperbolic and ordinary differential equations with delay
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 255-264

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In this paper, we consider an optimal control problem for a system of linear first-order hyperbolic equations in which the inhomogeneity in the right-hand side is determined from the controlled linear system of ordinary differential equations with constant delay. The coefficient matrix at phase variables in the system of ordinary differential equations depends on the control function. The cost functional is linear. On the basis of the exact increment formula (without remainder terms) of the cost functional, the problem is reduced to the optimal control problem of a system of ordinary differential equations. The result is formulated in the form of a non-classical variational optimality condition. The proposed problem reduction significantly reduces the amount of calculations when using numerical optimization methods. An illustrative example is given.
Keywords: hybrid problem, hyperbolic system, delayed system, variational optimality condition, problem reduction.
Mots-clés : exact increment formula 
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     title = {The non-classical optimality condition in the hybrid control problem of hyperbolic and ordinary differential equations with delay},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     url = {http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a9/}
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A. V. Arguchintsev; V. P. Poplevko. The non-classical optimality condition in the hybrid control problem of hyperbolic and ordinary differential equations with delay. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 255-264. http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a9/