Geodesic
On the search for a time-optimal boundary control using the method of moments for systems governed by the diffusion-wave equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 108-114

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For a system described by a one-dimensional, inhomogeneous diffusion-wave equation on a segment, two types of optimal boundary control problems are considered: the problem of finding a control with a minimum norm for a given control time and the problem of finding a control that brings the system to a given state in a minimum time under a given constraint on the norm of the control. Various ways of specifying conditions on the final state are considered. The finite-dimensional $l$-problem of moments is analyzed, to which the optimal control problem can be reduced. We show that under the conditions of well-posedness and solvability of this problem, the problem of finding a control with a minimum norm always has a solution, while the problem of finding a control with a minimum transition time may not have a solution.
Keywords: optimal control, Caputo derivative, $l$-moment problem.
Mots-clés : diffusion-wave equation 
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     author = {S. S. Postnov},
     title = {On the search for a time-optimal boundary control using the method of moments for systems governed by the diffusion-wave equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {108--114},
     publisher = {mathdoc},
     volume = {225},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_225_a8/}
}
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S. S. Postnov. On the search for a time-optimal boundary control using the method of moments for systems governed by the diffusion-wave equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 108-114. http://geodesic.mathdoc.fr/item/INTO_2023_225_a8/